QELM MASSIVE DATASET
License: MIT-like training text. No warranty. Educational and research use.
Topics: QELM, quantum computing, qubits, Qiskit, AI, ML, NLP, mathematics, optimization.
Notes: Text includes definitions, explanations, Q&A, pseudo-code, and doc-style notes.
QELM (Quantum-Enhanced Language Model) is an experimental framework that routes parts of a
transformer-like pipeline through parameterized quantum circuits. The project explores multi-block
quantum attention, feed-forward layers, sub-bit encoding where a scalar value is represented by the
pair (theta, phi), entropy-mixed gates, and parameter-shift gradients. The trainer aggregates token
embeddings, initializes statevectors, applies RY/RZ rotations and entangling gates, and measures the
resulting amplitudes. Residual connections and classical output projections produce logits over the
vocabulary.

Qiskit is an open-source SDK for working with quantum computers at the level of circuits,
algorithms,  and providers. Circuits are defined with QuantumCircuit, compiled with transpile, and
run on Aer simulators  or hardware backends such as IBM devices accessed via Qiskit Runtime. Noise
mitigation can include Pauli  twirling and zero-noise extrapolation (ZNE). Grover search, QAOA, VQE,
and primitives such as Sampler and  Estimator are available in the modern API.

A qubit is a two-level quantum system described by a state |psi> = alpha|0> + beta|1>, with
|alpha|^2 + |beta|^2 = 1. The Bloch sphere represents pure states via polar angle theta and
azimuthal angle phi. A rotation RY(theta) changes the  population between |0> and |1>, while RZ(phi)
adjusts the relative phase. Measurement in the computational basis collapses  the state with
probabilities given by the squared magnitudes of amplitudes.

Artificial intelligence models learn patterns from data. In language modeling, next-token prediction
minimizes cross-entropy between predicted distributions and observed tokens. Perplexity is
exp(cross-entropy)  and approximates the effective branching factor of the model. Smaller perplexity
implies better predictive power.

Key linear algebra concepts appear in both classical and quantum ML. Unitaries preserve inner
products;  Hermitian matrices have real eigenvalues; tensor products expand Hilbert space dimension
multiplicatively.  Gradient-based optimization typically uses Adam or variations of natural gradient
to adapt step sizes.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: How are attention weights approximated in QELM?
A: By entangling token qubits and analyzing marginal amplitude weights that correspond to contributions from tokens.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What does zero-noise extrapolation do?
A: It runs the same circuit at scaled noise levels, fits a curve, and extrapolates to the zero-noise limit.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is perplexity and how is it used?
A: Perplexity = exp(cross-entropy). It measures how well the model predicts tokens; lower is better.

Q: Why use parameter-shift gradients?
A: Because quantum circuits are non-linear in parameters but have tractable derivatives via shift rules. Evaluate the circuit at theta±s and compute the gradient from the difference.

Q: What is sub-bit encoding in QELM?
A: It maps a single scalar into a pair (theta, phi), encoding magnitude via RY and phase via RZ. Decoding estimates amplitudes to recover theta and phi, then maps back to a scalar.

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: Sub-Bit Encode/Decode
encode_scalar(x in [0,1]):
    theta = 2 * arcsin(sqrt(x))
    phi   = 2 * pi * x
    apply RY(theta); apply RZ(phi)

decode_scalar(state):
    estimate amplitudes -> recover theta_hat, phi_hat
    x_hat = (sin(theta_hat/2))^2

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: QELM Forward
emb = embeddings[input_id]
if positional: emb <- phase_shift(emb, position)
weights = quantum_attention(emb_sequence)
agg = sum(weights[t] * emb_sequence[t])
for block in blocks:
    agg <- QuantumTransformerBlock(agg)
logits = W_out * agg

PSEUDOCODE: Parameter-Shift Gradient
for each parameter i:
    theta_plus  = params[i] + s
    theta_minus = params[i] - s
    loss_plus   = run_circuit_and_loss(theta_plus)
    loss_minus  = run_circuit_and_loss(theta_minus)
    grad[i]     = 0.5 * (loss_plus - loss_minus)

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Positional: In QELM experiments, phase encoding is combined with small complex phase factors applied
per index. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Optimization: In QELM experiments, Adam and natural gradient is combined with stability on noisy
objectives. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Embedding: In QELM experiments, token vectors is combined with state initialization and rotations.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Context: In QELM experiments, conversation memory is combined with aggregated logits and residual
storage. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

Noise: In QELM experiments, decoherence and readout error is combined with mitigation via twirling
and extrapolation. The circuit depth is kept modest to limit simulation time, but entanglement is
preserved where useful. Parameter initialization uses small random values to avoid barren plateaus.
Training logs report gradient magnitudes, loss, and perplexity for transparency.

QAOA: In QELM experiments, cost and mixer Hamiltonians is combined with variational angles beta and
gamma. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Knowledge: In QELM experiments, matrix lookup is combined with retrieval vectors normalized on
output. The circuit depth is kept modest to limit simulation time, but entanglement is preserved
where useful. Parameter initialization uses small random values to avoid barren plateaus. Training
logs report gradient magnitudes, loss, and perplexity for transparency.

Grover: In QELM experiments, amplitude amplification is combined with oracle marking target states.
The circuit depth is kept modest to limit simulation time, but entanglement is preserved where
useful. Parameter initialization uses small random values to avoid barren plateaus. Training logs
report gradient magnitudes, loss, and perplexity for transparency.

GLOSSARY
--------
Amplitude: Complex coefficient of a basis state. Probability is the squared magnitude.
Ansatz: Parameterized circuit structure chosen for an optimization task.
Bloch Sphere: Geometric representation of pure qubit states as points on a unit sphere.
Entanglement: Non-classical correlations that cannot be described by separable states.
Parameter-Shift: Gradient estimation technique for gates with simple shift rules.
Perplexity: exp(cross-entropy), effective branching factor for language models.
RY Gate: Rotation around the Y axis; adjusts population between |0> and |1>.
RZ Gate: Rotation around the Z axis; changes phase between computational states.
Sub-Bit Encoding: Maps a scalar into angles (theta, phi) to expand representational capacity.
Transpile: Compilation step that maps a circuit onto a device basis with optimizations.

FACT 0: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 5: In QELM, logits are produced classically after quantum aggregation.
FACT 6: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 7: In QELM, logits are produced classically after quantum aggregation.
FACT 8: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 9: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 10: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 11: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 12: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 13: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 14: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 15: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 16: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 17: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 18: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 19: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 20: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 21: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 22: In QELM, logits are produced classically after quantum aggregation.
FACT 23: In QELM, logits are produced classically after quantum aggregation.
FACT 24: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 25: In QELM, logits are produced classically after quantum aggregation.
FACT 26: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 27: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 28: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 29: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 30: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 31: In QELM, logits are produced classically after quantum aggregation.
FACT 32: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 33: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 34: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 35: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 36: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 37: In QELM, logits are produced classically after quantum aggregation.
FACT 38: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 39: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 40: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 41: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 42: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 43: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 44: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 45: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 46: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 47: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 48: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 49: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 50: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 51: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 52: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 53: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 54: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 55: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 56: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 57: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 58: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 59: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 60: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 61: In QELM, logits are produced classically after quantum aggregation.
FACT 62: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 63: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 64: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 65: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 66: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 67: In QELM, logits are produced classically after quantum aggregation.
FACT 68: In QELM, logits are produced classically after quantum aggregation.
FACT 69: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 70: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 71: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 72: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 73: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 74: In QELM, logits are produced classically after quantum aggregation.
FACT 75: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 76: In QELM, logits are produced classically after quantum aggregation.
FACT 77: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 78: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 79: In QELM, logits are produced classically after quantum aggregation.
FACT 80: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 81: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 82: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 83: In QELM, logits are produced classically after quantum aggregation.
FACT 84: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 85: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 86: In QELM, logits are produced classically after quantum aggregation.
FACT 87: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 88: In QELM, logits are produced classically after quantum aggregation.
FACT 89: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 90: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 91: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 92: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 93: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 94: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 95: In QELM, logits are produced classically after quantum aggregation.
FACT 96: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 97: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 98: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 99: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 100: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 101: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 102: In QELM, logits are produced classically after quantum aggregation.
FACT 103: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 104: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 105: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 106: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 107: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 108: In QELM, logits are produced classically after quantum aggregation.
FACT 109: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 110: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 111: In QELM, logits are produced classically after quantum aggregation.
FACT 112: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 113: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 114: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 115: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 116: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 117: In QELM, logits are produced classically after quantum aggregation.
FACT 118: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 119: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 120: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 121: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 122: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 123: In QELM, logits are produced classically after quantum aggregation.
FACT 124: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 125: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 126: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 127: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 128: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 129: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 130: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 131: In QELM, logits are produced classically after quantum aggregation.
FACT 132: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 133: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 134: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 135: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 136: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 137: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 138: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 139: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 140: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 141: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 142: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 143: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 144: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 145: In QELM, logits are produced classically after quantum aggregation.
FACT 146: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 147: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 148: In QELM, logits are produced classically after quantum aggregation.
FACT 149: In QELM, logits are produced classically after quantum aggregation.
FACT 150: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 151: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 152: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 153: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 154: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 155: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 156: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 157: In QELM, logits are produced classically after quantum aggregation.
FACT 158: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 159: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 160: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 161: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 162: In QELM, logits are produced classically after quantum aggregation.
FACT 163: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 164: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 165: In QELM, logits are produced classically after quantum aggregation.
FACT 166: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 167: In QELM, logits are produced classically after quantum aggregation.
FACT 168: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 169: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 170: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 171: In QELM, logits are produced classically after quantum aggregation.
FACT 172: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 173: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 174: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 175: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 176: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 177: In QELM, logits are produced classically after quantum aggregation.
FACT 178: In QELM, logits are produced classically after quantum aggregation.
FACT 179: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 180: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 181: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 182: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 183: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 184: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 185: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 186: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 187: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 188: In QELM, logits are produced classically after quantum aggregation.
FACT 189: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 190: In QELM, logits are produced classically after quantum aggregation.
FACT 191: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 192: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 193: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 194: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 195: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 196: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 197: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 198: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 199: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 200: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 201: In QELM, logits are produced classically after quantum aggregation.
FACT 202: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 203: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 204: In QELM, logits are produced classically after quantum aggregation.
FACT 205: In QELM, logits are produced classically after quantum aggregation.
FACT 206: In QELM, logits are produced classically after quantum aggregation.
FACT 207: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 208: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 209: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 210: In QELM, logits are produced classically after quantum aggregation.
FACT 211: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 212: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 213: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 214: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 215: In QELM, logits are produced classically after quantum aggregation.
FACT 216: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 217: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 218: In QELM, logits are produced classically after quantum aggregation.
FACT 219: In QELM, logits are produced classically after quantum aggregation.
FACT 220: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 221: In QELM, logits are produced classically after quantum aggregation.
FACT 222: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 223: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 224: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 225: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 226: In QELM, logits are produced classically after quantum aggregation.
FACT 227: In QELM, logits are produced classically after quantum aggregation.
FACT 228: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 229: In QELM, logits are produced classically after quantum aggregation.
FACT 230: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 231: In QELM, logits are produced classically after quantum aggregation.
FACT 232: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 233: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 234: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 235: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 236: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 237: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 238: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 239: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 240: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 241: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 242: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 243: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 244: In QELM, logits are produced classically after quantum aggregation.
FACT 245: In QELM, logits are produced classically after quantum aggregation.
FACT 246: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 247: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 248: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 249: In QELM, logits are produced classically after quantum aggregation.
FACT 250: In QELM, logits are produced classically after quantum aggregation.
FACT 251: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 252: In QELM, logits are produced classically after quantum aggregation.
FACT 253: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 254: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 255: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 256: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 257: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 258: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 259: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 260: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 261: In QELM, logits are produced classically after quantum aggregation.
FACT 262: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 263: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 264: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 265: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 266: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 267: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 268: In QELM, logits are produced classically after quantum aggregation.
FACT 269: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 270: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 271: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 272: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 273: In QELM, logits are produced classically after quantum aggregation.
FACT 274: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 275: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 276: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 277: In QELM, logits are produced classically after quantum aggregation.
FACT 278: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 279: In QELM, logits are produced classically after quantum aggregation.
FACT 280: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 281: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 282: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 283: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 284: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 285: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 286: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 287: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 288: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 289: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 290: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 291: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 292: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 293: In QELM, logits are produced classically after quantum aggregation.
FACT 294: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 295: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 296: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 297: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 298: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 299: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 300: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 301: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 302: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 303: In QELM, logits are produced classically after quantum aggregation.
FACT 304: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 305: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 306: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 307: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 308: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 309: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 310: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 311: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 312: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 313: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 314: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 315: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 316: In QELM, logits are produced classically after quantum aggregation.
FACT 317: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 318: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 319: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 320: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 321: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 322: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 323: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 324: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 325: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 326: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 327: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 328: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 329: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 330: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 331: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 332: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 333: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 334: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 335: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 336: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 337: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 338: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 339: In QELM, logits are produced classically after quantum aggregation.
FACT 340: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 341: In QELM, logits are produced classically after quantum aggregation.
FACT 342: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 343: In QELM, logits are produced classically after quantum aggregation.
FACT 344: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 345: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 346: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 347: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 348: In QELM, logits are produced classically after quantum aggregation.
FACT 349: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 350: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 351: In QELM, logits are produced classically after quantum aggregation.
FACT 352: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 353: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 354: In QELM, logits are produced classically after quantum aggregation.
FACT 355: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 356: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 357: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 358: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 359: In QELM, logits are produced classically after quantum aggregation.
FACT 360: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 361: In QELM, logits are produced classically after quantum aggregation.
FACT 362: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 363: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 364: In QELM, logits are produced classically after quantum aggregation.
FACT 365: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 366: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 367: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 368: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 369: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 370: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 371: In QELM, logits are produced classically after quantum aggregation.
FACT 372: In QELM, logits are produced classically after quantum aggregation.
FACT 373: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 374: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 375: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 376: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 377: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 378: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 379: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 380: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 381: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 382: In QELM, logits are produced classically after quantum aggregation.
FACT 383: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 384: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 385: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 386: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 387: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 388: In QELM, logits are produced classically after quantum aggregation.
FACT 389: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 390: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 391: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 392: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 393: In QELM, logits are produced classically after quantum aggregation.
FACT 394: In QELM, logits are produced classically after quantum aggregation.
FACT 395: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 396: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 397: In QELM, logits are produced classically after quantum aggregation.
FACT 398: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 399: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 400: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 401: In QELM, logits are produced classically after quantum aggregation.
FACT 402: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 403: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 404: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 405: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 406: In QELM, logits are produced classically after quantum aggregation.
FACT 407: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 408: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 409: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 410: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 411: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 412: In QELM, logits are produced classically after quantum aggregation.
FACT 413: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 414: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 415: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 416: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 417: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 418: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 419: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 420: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 421: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 422: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 423: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 424: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 425: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 426: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 427: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 428: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 429: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 430: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 431: In QELM, logits are produced classically after quantum aggregation.
FACT 432: In QELM, logits are produced classically after quantum aggregation.
FACT 433: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 434: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 435: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 436: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 437: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 438: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 439: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 440: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 441: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 442: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 443: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 444: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 445: In QELM, logits are produced classically after quantum aggregation.
FACT 446: In QELM, logits are produced classically after quantum aggregation.
FACT 447: In QELM, logits are produced classically after quantum aggregation.
FACT 448: In QELM, logits are produced classically after quantum aggregation.
FACT 449: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 450: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 451: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 452: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 453: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 454: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 455: In QELM, logits are produced classically after quantum aggregation.
FACT 456: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 457: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 458: In QELM, logits are produced classically after quantum aggregation.
FACT 459: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 460: In QELM, logits are produced classically after quantum aggregation.
FACT 461: In QELM, logits are produced classically after quantum aggregation.
FACT 462: In QELM, logits are produced classically after quantum aggregation.
FACT 463: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 464: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 465: In QELM, logits are produced classically after quantum aggregation.
FACT 466: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 467: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 468: In QELM, logits are produced classically after quantum aggregation.
FACT 469: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 470: In QELM, logits are produced classically after quantum aggregation.
FACT 471: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 472: In QELM, logits are produced classically after quantum aggregation.
FACT 473: In QELM, logits are produced classically after quantum aggregation.
FACT 474: In QELM, logits are produced classically after quantum aggregation.
FACT 475: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 476: In QELM, logits are produced classically after quantum aggregation.
FACT 477: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 478: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 479: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 480: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 481: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 482: In QELM, logits are produced classically after quantum aggregation.
FACT 483: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 484: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 485: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 486: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 487: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 488: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 489: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 490: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 491: In QELM, logits are produced classically after quantum aggregation.
FACT 492: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 493: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 494: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 495: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 496: In QELM, logits are produced classically after quantum aggregation.
FACT 497: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 498: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 499: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 500: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 501: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 502: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 503: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 504: In QELM, logits are produced classically after quantum aggregation.
FACT 505: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 506: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 507: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 508: In QELM, logits are produced classically after quantum aggregation.
FACT 509: In QELM, logits are produced classically after quantum aggregation.
FACT 510: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 511: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 512: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 513: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 514: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 515: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 516: In QELM, logits are produced classically after quantum aggregation.
FACT 517: In QELM, logits are produced classically after quantum aggregation.
FACT 518: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 519: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 520: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 521: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 522: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 523: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 524: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 525: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 526: In QELM, logits are produced classically after quantum aggregation.
FACT 527: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 528: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 529: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 530: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 531: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 532: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 533: In QELM, logits are produced classically after quantum aggregation.
FACT 534: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 535: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 536: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 537: In QELM, logits are produced classically after quantum aggregation.
FACT 538: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 539: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 540: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 541: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 542: In QELM, logits are produced classically after quantum aggregation.
FACT 543: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 544: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 545: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 546: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 547: In QELM, logits are produced classically after quantum aggregation.
FACT 548: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 549: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 550: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 551: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 552: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 553: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 554: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 555: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 556: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 557: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 558: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 559: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 560: In QELM, logits are produced classically after quantum aggregation.
FACT 561: In QELM, logits are produced classically after quantum aggregation.
FACT 562: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 563: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 564: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 565: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 566: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 567: In QELM, logits are produced classically after quantum aggregation.
FACT 568: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 569: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 570: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 571: In QELM, logits are produced classically after quantum aggregation.
FACT 572: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 573: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 574: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 575: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 576: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 577: In QELM, logits are produced classically after quantum aggregation.
FACT 578: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 579: In QELM, logits are produced classically after quantum aggregation.
FACT 580: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 581: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 582: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 583: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 584: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 585: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 586: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 587: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 588: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 589: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 590: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 591: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 592: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 593: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 594: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 595: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 596: In QELM, logits are produced classically after quantum aggregation.
FACT 597: In QELM, logits are produced classically after quantum aggregation.
FACT 598: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 599: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 600: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 601: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 602: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 603: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 604: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 605: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 606: In QELM, logits are produced classically after quantum aggregation.
FACT 607: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 608: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 609: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 610: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 611: In QELM, logits are produced classically after quantum aggregation.
FACT 612: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 613: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 614: In QELM, logits are produced classically after quantum aggregation.
FACT 615: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 616: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 617: In QELM, logits are produced classically after quantum aggregation.
FACT 618: In QELM, logits are produced classically after quantum aggregation.
FACT 619: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 620: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 621: In QELM, logits are produced classically after quantum aggregation.
FACT 622: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 623: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 624: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 625: In QELM, logits are produced classically after quantum aggregation.
FACT 626: In QELM, logits are produced classically after quantum aggregation.
FACT 627: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 628: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 629: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 630: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 631: In QELM, logits are produced classically after quantum aggregation.
FACT 632: In QELM, logits are produced classically after quantum aggregation.
FACT 633: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 634: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 635: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 636: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 637: In QELM, logits are produced classically after quantum aggregation.
FACT 638: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 639: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 640: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 641: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 642: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 643: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 644: In QELM, logits are produced classically after quantum aggregation.
FACT 645: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 646: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 647: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 648: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 649: In QELM, logits are produced classically after quantum aggregation.
FACT 650: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 651: In QELM, logits are produced classically after quantum aggregation.
FACT 652: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 653: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 654: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 655: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 656: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 657: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 658: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 659: In QELM, logits are produced classically after quantum aggregation.
FACT 660: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 661: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 662: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 663: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 664: In QELM, logits are produced classically after quantum aggregation.
FACT 665: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 666: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 667: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 668: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 669: In QELM, logits are produced classically after quantum aggregation.
FACT 670: In QELM, logits are produced classically after quantum aggregation.
FACT 671: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 672: In QELM, logits are produced classically after quantum aggregation.
FACT 673: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 674: In QELM, logits are produced classically after quantum aggregation.
FACT 675: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 676: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 677: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 678: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 679: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 680: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 681: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 682: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 683: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 684: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 685: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 686: In QELM, logits are produced classically after quantum aggregation.
FACT 687: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 688: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 689: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 690: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 691: In QELM, logits are produced classically after quantum aggregation.
FACT 692: In QELM, logits are produced classically after quantum aggregation.
FACT 693: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 694: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 695: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 696: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 697: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 698: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 699: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 700: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 701: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 702: In QELM, logits are produced classically after quantum aggregation.
FACT 703: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 704: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 705: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 706: In QELM, logits are produced classically after quantum aggregation.
FACT 707: In QELM, logits are produced classically after quantum aggregation.
FACT 708: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 709: In QELM, logits are produced classically after quantum aggregation.
FACT 710: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 711: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 712: In QELM, logits are produced classically after quantum aggregation.
FACT 713: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 714: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 715: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 716: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 717: In QELM, logits are produced classically after quantum aggregation.
FACT 718: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 719: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 720: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 721: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 722: In QELM, logits are produced classically after quantum aggregation.
FACT 723: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 724: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 725: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 726: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 727: In QELM, logits are produced classically after quantum aggregation.
FACT 728: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 729: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 730: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 731: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 732: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 733: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 734: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 735: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 736: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 737: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 738: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 739: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 740: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 741: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 742: In QELM, logits are produced classically after quantum aggregation.
FACT 743: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 744: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 745: In QELM, logits are produced classically after quantum aggregation.
FACT 746: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 747: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 748: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 749: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 750: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 751: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 752: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 753: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 754: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 755: In QELM, logits are produced classically after quantum aggregation.
FACT 756: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 757: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 758: In QELM, logits are produced classically after quantum aggregation.
FACT 759: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 760: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 761: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 762: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 763: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 764: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 765: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 766: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 767: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 768: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 769: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 770: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 771: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 772: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 773: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 774: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 775: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 776: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 777: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 778: In QELM, logits are produced classically after quantum aggregation.
FACT 779: In QELM, logits are produced classically after quantum aggregation.
FACT 780: In QELM, logits are produced classically after quantum aggregation.
FACT 781: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 782: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 783: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 784: In QELM, logits are produced classically after quantum aggregation.
FACT 785: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 786: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 787: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 788: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 789: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 790: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 791: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 792: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 793: In QELM, logits are produced classically after quantum aggregation.
FACT 794: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 795: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 796: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 797: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 798: In QELM, logits are produced classically after quantum aggregation.
FACT 799: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 800: In QELM, logits are produced classically after quantum aggregation.
FACT 801: In QELM, logits are produced classically after quantum aggregation.
FACT 802: In QELM, logits are produced classically after quantum aggregation.
FACT 803: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 804: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 805: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 806: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 807: In QELM, logits are produced classically after quantum aggregation.
FACT 808: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 809: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 810: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 811: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 812: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 813: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 814: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 815: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 816: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 817: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 818: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 819: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 820: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 821: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 822: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 823: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 824: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 825: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 826: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 827: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 828: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 829: In QELM, logits are produced classically after quantum aggregation.
FACT 830: In QELM, logits are produced classically after quantum aggregation.
FACT 831: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 832: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 833: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 834: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 835: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 836: In QELM, logits are produced classically after quantum aggregation.
FACT 837: In QELM, logits are produced classically after quantum aggregation.
FACT 838: In QELM, logits are produced classically after quantum aggregation.
FACT 839: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 840: In QELM, logits are produced classically after quantum aggregation.
FACT 841: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 842: In QELM, logits are produced classically after quantum aggregation.
FACT 843: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 844: In QELM, logits are produced classically after quantum aggregation.
FACT 845: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 846: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 847: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 848: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 849: In QELM, logits are produced classically after quantum aggregation.
FACT 850: In QELM, logits are produced classically after quantum aggregation.
FACT 851: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 852: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 853: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 854: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 855: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 856: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 857: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 858: In QELM, logits are produced classically after quantum aggregation.
FACT 859: In QELM, logits are produced classically after quantum aggregation.
FACT 860: In QELM, logits are produced classically after quantum aggregation.
FACT 861: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 862: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 863: In QELM, logits are produced classically after quantum aggregation.
FACT 864: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 865: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 866: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 867: In QELM, logits are produced classically after quantum aggregation.
FACT 868: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 869: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 870: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 871: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 872: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 873: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 874: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 875: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 876: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 877: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 878: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 879: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 880: In QELM, logits are produced classically after quantum aggregation.
FACT 881: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 882: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 883: In QELM, logits are produced classically after quantum aggregation.
FACT 884: In QELM, logits are produced classically after quantum aggregation.
FACT 885: In QELM, logits are produced classically after quantum aggregation.
FACT 886: In QELM, logits are produced classically after quantum aggregation.
FACT 887: In QELM, logits are produced classically after quantum aggregation.
FACT 888: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 889: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 890: In QELM, logits are produced classically after quantum aggregation.
FACT 891: In QELM, logits are produced classically after quantum aggregation.
FACT 892: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 893: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 894: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 895: In QELM, logits are produced classically after quantum aggregation.
FACT 896: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 897: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 898: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 899: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 900: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 901: In QELM, logits are produced classically after quantum aggregation.
FACT 902: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 903: In QELM, logits are produced classically after quantum aggregation.
FACT 904: In QELM, logits are produced classically after quantum aggregation.
FACT 905: In QELM, logits are produced classically after quantum aggregation.
FACT 906: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 907: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 908: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 909: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 910: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 911: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 912: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 913: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 914: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 915: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 916: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 917: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 918: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 919: In QELM, logits are produced classically after quantum aggregation.
FACT 920: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 921: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 922: In QELM, logits are produced classically after quantum aggregation.
FACT 923: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 924: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 925: In QELM, logits are produced classically after quantum aggregation.
FACT 926: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 927: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 928: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 929: In QELM, logits are produced classically after quantum aggregation.
FACT 930: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 931: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 932: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 933: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 934: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 935: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 936: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 937: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 938: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 939: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 940: In QELM, logits are produced classically after quantum aggregation.
FACT 941: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 942: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 943: In QELM, logits are produced classically after quantum aggregation.
FACT 944: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 945: In QELM, logits are produced classically after quantum aggregation.
FACT 946: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 947: In QELM, logits are produced classically after quantum aggregation.
FACT 948: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 949: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 950: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 951: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 952: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 953: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 954: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 955: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 956: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 957: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 958: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 959: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 960: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 961: In QELM, logits are produced classically after quantum aggregation.
FACT 962: In QELM, logits are produced classically after quantum aggregation.
FACT 963: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 964: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 965: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 966: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 967: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 968: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 969: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 970: In QELM, logits are produced classically after quantum aggregation.
FACT 971: In QELM, logits are produced classically after quantum aggregation.
FACT 972: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 973: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 974: In QELM, logits are produced classically after quantum aggregation.
FACT 975: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 976: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 977: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 978: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 979: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 980: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 981: In QELM, logits are produced classically after quantum aggregation.
FACT 982: In QELM, logits are produced classically after quantum aggregation.
FACT 983: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 984: In QELM, logits are produced classically after quantum aggregation.
FACT 985: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 986: In QELM, logits are produced classically after quantum aggregation.
FACT 987: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 988: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 989: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 990: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 991: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 992: In QELM, logits are produced classically after quantum aggregation.
FACT 993: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 994: In QELM, logits are produced classically after quantum aggregation.
FACT 995: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 996: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 997: In QELM, logits are produced classically after quantum aggregation.
FACT 998: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 999: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1000: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1001: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1002: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1003: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1004: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1005: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1006: In QELM, logits are produced classically after quantum aggregation.
FACT 1007: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1008: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1009: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1010: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1011: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1012: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1013: In QELM, logits are produced classically after quantum aggregation.
FACT 1014: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1015: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1016: In QELM, logits are produced classically after quantum aggregation.
FACT 1017: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1018: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1019: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1020: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1021: In QELM, logits are produced classically after quantum aggregation.
FACT 1022: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1023: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1024: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1025: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1026: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1027: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1028: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1029: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1030: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1031: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1032: In QELM, logits are produced classically after quantum aggregation.
FACT 1033: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1034: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1035: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1036: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1037: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1038: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1039: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1040: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1041: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1042: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1043: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1044: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1045: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1046: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1047: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1048: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1049: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1050: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1051: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1052: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1053: In QELM, logits are produced classically after quantum aggregation.
FACT 1054: In QELM, logits are produced classically after quantum aggregation.
FACT 1055: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1056: In QELM, logits are produced classically after quantum aggregation.
FACT 1057: In QELM, logits are produced classically after quantum aggregation.
FACT 1058: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1059: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1060: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1061: In QELM, logits are produced classically after quantum aggregation.
FACT 1062: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1063: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1064: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1065: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1066: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1067: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1068: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1069: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1070: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1071: In QELM, logits are produced classically after quantum aggregation.
FACT 1072: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1073: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1074: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1075: In QELM, logits are produced classically after quantum aggregation.
FACT 1076: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1077: In QELM, logits are produced classically after quantum aggregation.
FACT 1078: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1079: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1080: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1081: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1082: In QELM, logits are produced classically after quantum aggregation.
FACT 1083: In QELM, logits are produced classically after quantum aggregation.
FACT 1084: In QELM, logits are produced classically after quantum aggregation.
FACT 1085: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1086: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1087: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1088: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1089: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1090: In QELM, logits are produced classically after quantum aggregation.
FACT 1091: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1092: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1093: In QELM, logits are produced classically after quantum aggregation.
FACT 1094: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1095: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1096: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1097: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1098: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1099: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1100: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1101: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1102: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1103: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1104: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1105: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1106: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1107: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1108: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1109: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1110: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1111: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1112: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1113: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1114: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1115: In QELM, logits are produced classically after quantum aggregation.
FACT 1116: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1117: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1118: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1119: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1120: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1121: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1122: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1123: In QELM, logits are produced classically after quantum aggregation.
FACT 1124: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1125: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1126: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1127: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1128: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1129: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1130: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1131: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1132: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1133: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1134: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1135: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1136: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1137: In QELM, logits are produced classically after quantum aggregation.
FACT 1138: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1139: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1140: In QELM, logits are produced classically after quantum aggregation.
FACT 1141: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1142: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1143: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1144: In QELM, logits are produced classically after quantum aggregation.
FACT 1145: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1146: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1147: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1148: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1149: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1150: In QELM, logits are produced classically after quantum aggregation.
FACT 1151: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1152: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1153: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1154: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1155: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1156: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1157: In QELM, logits are produced classically after quantum aggregation.
FACT 1158: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1159: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1160: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1161: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1162: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1163: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1164: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1165: In QELM, logits are produced classically after quantum aggregation.
FACT 1166: In QELM, logits are produced classically after quantum aggregation.
FACT 1167: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1168: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1169: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1170: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1171: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1172: In QELM, logits are produced classically after quantum aggregation.
FACT 1173: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1174: In QELM, logits are produced classically after quantum aggregation.
FACT 1175: In QELM, logits are produced classically after quantum aggregation.
FACT 1176: In QELM, logits are produced classically after quantum aggregation.
FACT 1177: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1178: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1179: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1180: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1181: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1182: In QELM, logits are produced classically after quantum aggregation.
FACT 1183: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1184: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1185: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1186: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1187: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1188: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1189: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1190: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1191: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1192: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1193: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1194: In QELM, logits are produced classically after quantum aggregation.
FACT 1195: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1196: In QELM, logits are produced classically after quantum aggregation.
FACT 1197: In QELM, logits are produced classically after quantum aggregation.
FACT 1198: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1199: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1200: In QELM, logits are produced classically after quantum aggregation.
FACT 1201: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1202: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1203: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1204: In QELM, logits are produced classically after quantum aggregation.
FACT 1205: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1206: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1207: In QELM, logits are produced classically after quantum aggregation.
FACT 1208: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1209: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1210: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1211: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1212: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1213: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1214: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1215: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1216: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1217: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1218: In QELM, logits are produced classically after quantum aggregation.
FACT 1219: In QELM, logits are produced classically after quantum aggregation.
FACT 1220: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1221: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1222: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1223: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1224: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1225: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1226: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1227: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1228: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1229: In QELM, logits are produced classically after quantum aggregation.
FACT 1230: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1231: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1232: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1233: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1234: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1235: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1236: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1237: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1238: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1239: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1240: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1241: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1242: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1243: In QELM, logits are produced classically after quantum aggregation.
FACT 1244: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1245: In QELM, logits are produced classically after quantum aggregation.
FACT 1246: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1247: In QELM, logits are produced classically after quantum aggregation.
FACT 1248: In QELM, logits are produced classically after quantum aggregation.
FACT 1249: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1250: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1251: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1252: In QELM, logits are produced classically after quantum aggregation.
FACT 1253: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1254: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1255: In QELM, logits are produced classically after quantum aggregation.
FACT 1256: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1257: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1258: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1259: In QELM, logits are produced classically after quantum aggregation.
FACT 1260: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1261: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1262: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1263: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1264: In QELM, logits are produced classically after quantum aggregation.
FACT 1265: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1266: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1267: In QELM, logits are produced classically after quantum aggregation.
FACT 1268: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1269: In QELM, logits are produced classically after quantum aggregation.
FACT 1270: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1271: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1272: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1273: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1274: In QELM, logits are produced classically after quantum aggregation.
FACT 1275: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1276: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1277: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1278: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1279: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1280: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1281: In QELM, logits are produced classically after quantum aggregation.
FACT 1282: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1283: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1284: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1285: In QELM, logits are produced classically after quantum aggregation.
FACT 1286: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1287: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1288: In QELM, logits are produced classically after quantum aggregation.
FACT 1289: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1290: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1291: In QELM, logits are produced classically after quantum aggregation.
FACT 1292: In QELM, logits are produced classically after quantum aggregation.
FACT 1293: In QELM, logits are produced classically after quantum aggregation.
FACT 1294: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1295: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1296: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1297: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1298: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1299: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1300: In QELM, logits are produced classically after quantum aggregation.
FACT 1301: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1302: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1303: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1304: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1305: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1306: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1307: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1308: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1309: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1310: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1311: In QELM, logits are produced classically after quantum aggregation.
FACT 1312: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1313: In QELM, logits are produced classically after quantum aggregation.
FACT 1314: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1315: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1316: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1317: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1318: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1319: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1320: In QELM, logits are produced classically after quantum aggregation.
FACT 1321: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1322: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1323: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1324: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1325: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1326: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1327: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1328: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1329: In QELM, logits are produced classically after quantum aggregation.
FACT 1330: In QELM, logits are produced classically after quantum aggregation.
FACT 1331: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1332: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1333: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1334: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1335: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1336: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1337: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1338: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1339: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1340: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1341: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1342: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1343: In QELM, logits are produced classically after quantum aggregation.
FACT 1344: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1345: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1346: In QELM, logits are produced classically after quantum aggregation.
FACT 1347: In QELM, logits are produced classically after quantum aggregation.
FACT 1348: In QELM, logits are produced classically after quantum aggregation.
FACT 1349: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1350: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1351: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1352: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1353: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1354: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1355: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1356: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1357: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1358: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1359: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1360: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1361: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1362: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1363: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1364: In QELM, logits are produced classically after quantum aggregation.
FACT 1365: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1366: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1367: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1368: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1369: In QELM, logits are produced classically after quantum aggregation.
FACT 1370: In QELM, logits are produced classically after quantum aggregation.
FACT 1371: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1372: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1373: In QELM, logits are produced classically after quantum aggregation.
FACT 1374: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1375: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1376: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1377: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1378: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1379: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1380: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1381: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1382: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1383: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1384: In QELM, logits are produced classically after quantum aggregation.
FACT 1385: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1386: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1387: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1388: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1389: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1390: In QELM, logits are produced classically after quantum aggregation.
FACT 1391: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1392: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1393: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1394: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1395: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1396: In QELM, logits are produced classically after quantum aggregation.
FACT 1397: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1398: In QELM, logits are produced classically after quantum aggregation.
FACT 1399: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1400: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1401: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1402: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1403: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1404: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1405: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1406: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1407: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1408: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1409: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1410: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1411: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1412: In QELM, logits are produced classically after quantum aggregation.
FACT 1413: In QELM, logits are produced classically after quantum aggregation.
FACT 1414: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1415: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1416: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1417: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1418: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1419: In QELM, logits are produced classically after quantum aggregation.
FACT 1420: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1421: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1422: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1423: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1424: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1425: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1426: In QELM, logits are produced classically after quantum aggregation.
FACT 1427: In QELM, logits are produced classically after quantum aggregation.
FACT 1428: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1429: In QELM, logits are produced classically after quantum aggregation.
FACT 1430: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1431: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1432: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1433: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1434: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1435: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1436: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1437: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1438: In QELM, logits are produced classically after quantum aggregation.
FACT 1439: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1440: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1441: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1442: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1443: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1444: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1445: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1446: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1447: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1448: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1449: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1450: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1451: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1452: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1453: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1454: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1455: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1456: In QELM, logits are produced classically after quantum aggregation.
FACT 1457: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1458: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1459: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1460: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1461: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1462: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1463: In QELM, logits are produced classically after quantum aggregation.
FACT 1464: In QELM, logits are produced classically after quantum aggregation.
FACT 1465: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1466: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1467: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1468: In QELM, logits are produced classically after quantum aggregation.
FACT 1469: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1470: In QELM, logits are produced classically after quantum aggregation.
FACT 1471: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1472: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1473: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1474: In QELM, logits are produced classically after quantum aggregation.
FACT 1475: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1476: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1477: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1478: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1479: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1480: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1481: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1482: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1483: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1484: In QELM, logits are produced classically after quantum aggregation.
FACT 1485: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1486: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1487: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1488: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1489: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1490: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1491: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1492: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1493: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1494: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1495: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1496: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1497: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1498: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1499: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1500: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1501: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1502: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1503: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1504: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1505: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1506: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1507: In QELM, logits are produced classically after quantum aggregation.
FACT 1508: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1509: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1510: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1511: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1512: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1513: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1514: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1515: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1516: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1517: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1518: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1519: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1520: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1521: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1522: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1523: In QELM, logits are produced classically after quantum aggregation.
FACT 1524: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1525: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1526: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1527: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1528: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1529: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1530: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1531: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1532: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1533: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1534: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1535: In QELM, logits are produced classically after quantum aggregation.
FACT 1536: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1537: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1538: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1539: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1540: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1541: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1542: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1543: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1544: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1545: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1546: In QELM, logits are produced classically after quantum aggregation.
FACT 1547: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1548: In QELM, logits are produced classically after quantum aggregation.
FACT 1549: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1550: In QELM, logits are produced classically after quantum aggregation.
FACT 1551: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1552: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1553: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1554: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1555: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1556: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1557: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1558: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1559: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1560: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1561: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1562: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1563: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1564: In QELM, logits are produced classically after quantum aggregation.
FACT 1565: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1566: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1567: In QELM, logits are produced classically after quantum aggregation.
FACT 1568: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1569: In QELM, logits are produced classically after quantum aggregation.
FACT 1570: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1571: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1572: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1573: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1574: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1575: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1576: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1577: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1578: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1579: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1580: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1581: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1582: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1583: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1584: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1585: In QELM, logits are produced classically after quantum aggregation.
FACT 1586: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1587: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1588: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1589: In QELM, logits are produced classically after quantum aggregation.
FACT 1590: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1591: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1592: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1593: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1594: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1595: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1596: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1597: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1598: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1599: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1600: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1601: In QELM, logits are produced classically after quantum aggregation.
FACT 1602: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1603: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1604: In QELM, logits are produced classically after quantum aggregation.
FACT 1605: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1606: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1607: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1608: In QELM, logits are produced classically after quantum aggregation.
FACT 1609: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1610: In QELM, logits are produced classically after quantum aggregation.
FACT 1611: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1612: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1613: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1614: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1615: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1616: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1617: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1618: In QELM, logits are produced classically after quantum aggregation.
FACT 1619: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1620: In QELM, logits are produced classically after quantum aggregation.
FACT 1621: In QELM, logits are produced classically after quantum aggregation.
FACT 1622: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1623: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1624: In QELM, logits are produced classically after quantum aggregation.
FACT 1625: In QELM, logits are produced classically after quantum aggregation.
FACT 1626: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1627: In QELM, logits are produced classically after quantum aggregation.
FACT 1628: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1629: In QELM, logits are produced classically after quantum aggregation.
FACT 1630: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1631: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1632: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1633: In QELM, logits are produced classically after quantum aggregation.
FACT 1634: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1635: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1636: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1637: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1638: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1639: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1640: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1641: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1642: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1643: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1644: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1645: In QELM, logits are produced classically after quantum aggregation.
FACT 1646: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1647: In QELM, logits are produced classically after quantum aggregation.
FACT 1648: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1649: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1650: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1651: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1652: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1653: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1654: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1655: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1656: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1657: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1658: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1659: In QELM, logits are produced classically after quantum aggregation.
FACT 1660: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1661: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1662: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1663: In QELM, logits are produced classically after quantum aggregation.
FACT 1664: In QELM, logits are produced classically after quantum aggregation.
FACT 1665: In QELM, logits are produced classically after quantum aggregation.
FACT 1666: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1667: In QELM, logits are produced classically after quantum aggregation.
FACT 1668: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1669: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1670: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1671: In QELM, logits are produced classically after quantum aggregation.
FACT 1672: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1673: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1674: In QELM, logits are produced classically after quantum aggregation.
FACT 1675: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1676: In QELM, logits are produced classically after quantum aggregation.
FACT 1677: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1678: In QELM, logits are produced classically after quantum aggregation.
FACT 1679: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1680: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1681: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1682: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1683: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1684: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1685: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1686: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1687: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1688: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1689: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1690: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1691: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1692: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1693: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1694: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1695: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1696: In QELM, logits are produced classically after quantum aggregation.
FACT 1697: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1698: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1699: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1700: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1701: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1702: In QELM, logits are produced classically after quantum aggregation.
FACT 1703: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1704: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1705: In QELM, logits are produced classically after quantum aggregation.
FACT 1706: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1707: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1708: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1709: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1710: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1711: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1712: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1713: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1714: In QELM, logits are produced classically after quantum aggregation.
FACT 1715: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1716: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1717: In QELM, logits are produced classically after quantum aggregation.
FACT 1718: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1719: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1720: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1721: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1722: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1723: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1724: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1725: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1726: In QELM, logits are produced classically after quantum aggregation.
FACT 1727: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1728: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1729: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1730: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1731: In QELM, logits are produced classically after quantum aggregation.
FACT 1732: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1733: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1734: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1735: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1736: In QELM, logits are produced classically after quantum aggregation.
FACT 1737: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1738: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1739: In QELM, logits are produced classically after quantum aggregation.
FACT 1740: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1741: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1742: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1743: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1744: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1745: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1746: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1747: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1748: In QELM, logits are produced classically after quantum aggregation.
FACT 1749: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1750: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1751: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1752: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1753: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1754: In QELM, logits are produced classically after quantum aggregation.
FACT 1755: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1756: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1757: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1758: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1759: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1760: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1761: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1762: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1763: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1764: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1765: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1766: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1767: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1768: In QELM, logits are produced classically after quantum aggregation.
FACT 1769: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1770: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1771: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1772: In QELM, logits are produced classically after quantum aggregation.
FACT 1773: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1774: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1775: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1776: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1777: In QELM, logits are produced classically after quantum aggregation.
FACT 1778: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1779: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1780: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1781: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1782: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1783: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1784: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1785: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1786: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1787: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1788: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1789: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1790: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1791: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1792: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1793: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1794: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1795: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1796: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1797: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1798: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1799: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1800: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1801: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1802: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1803: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1804: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1805: In QELM, logits are produced classically after quantum aggregation.
FACT 1806: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1807: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1808: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1809: In QELM, logits are produced classically after quantum aggregation.
FACT 1810: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1811: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1812: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1813: In QELM, logits are produced classically after quantum aggregation.
FACT 1814: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1815: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1816: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1817: In QELM, logits are produced classically after quantum aggregation.
FACT 1818: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1819: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1820: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1821: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1822: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1823: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1824: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1825: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1826: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1827: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1828: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1829: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1830: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1831: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1832: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1833: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1834: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1835: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1836: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1837: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1838: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1839: In QELM, logits are produced classically after quantum aggregation.
FACT 1840: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1841: In QELM, logits are produced classically after quantum aggregation.
FACT 1842: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1843: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1844: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1845: In QELM, logits are produced classically after quantum aggregation.
FACT 1846: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1847: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1848: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1849: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1850: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1851: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1852: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1853: In QELM, logits are produced classically after quantum aggregation.
FACT 1854: In QELM, logits are produced classically after quantum aggregation.
FACT 1855: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1856: In QELM, logits are produced classically after quantum aggregation.
FACT 1857: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1858: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1859: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1860: In QELM, logits are produced classically after quantum aggregation.
FACT 1861: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1862: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1863: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1864: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1865: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1866: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1867: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1868: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1869: In QELM, logits are produced classically after quantum aggregation.
FACT 1870: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1871: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1872: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1873: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1874: In QELM, logits are produced classically after quantum aggregation.
FACT 1875: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1876: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1877: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1878: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1879: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1880: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1881: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1882: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1883: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1884: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1885: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1886: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1887: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1888: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1889: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1890: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1891: In QELM, logits are produced classically after quantum aggregation.
FACT 1892: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1893: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1894: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1895: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1896: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1897: In QELM, logits are produced classically after quantum aggregation.
FACT 1898: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1899: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1900: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1901: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1902: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1903: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1904: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1905: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1906: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1907: In QELM, logits are produced classically after quantum aggregation.
FACT 1908: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1909: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1910: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1911: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1912: In QELM, logits are produced classically after quantum aggregation.
FACT 1913: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1914: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1915: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1916: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1917: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1918: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1919: In QELM, logits are produced classically after quantum aggregation.
FACT 1920: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1921: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1922: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1923: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1924: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1925: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1926: In QELM, logits are produced classically after quantum aggregation.
FACT 1927: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1928: In QELM, logits are produced classically after quantum aggregation.
FACT 1929: In QELM, logits are produced classically after quantum aggregation.
FACT 1930: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1931: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1932: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1933: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1934: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1935: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1936: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1937: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1938: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1939: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1940: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1941: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1942: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1943: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1944: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1945: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1946: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1947: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1948: In QELM, logits are produced classically after quantum aggregation.
FACT 1949: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1950: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1951: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1952: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1953: In QELM, logits are produced classically after quantum aggregation.
FACT 1954: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1955: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1956: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1957: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1958: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1959: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1960: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1961: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1962: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1963: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1964: In QELM, logits are produced classically after quantum aggregation.
FACT 1965: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1966: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1967: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1968: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1969: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1970: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1971: In QELM, logits are produced classically after quantum aggregation.
FACT 1972: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1973: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1974: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1975: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1976: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1977: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1978: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1979: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1980: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1981: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1982: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1983: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1984: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1985: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1986: In QELM, logits are produced classically after quantum aggregation.
FACT 1987: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1988: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1989: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1990: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1991: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 1992: In QELM, logits are produced classically after quantum aggregation.
FACT 1993: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1994: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1995: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 1996: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 1997: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1998: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 1999: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2000: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2001: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2002: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2003: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2004: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2005: In QELM, logits are produced classically after quantum aggregation.
FACT 2006: In QELM, logits are produced classically after quantum aggregation.
FACT 2007: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2008: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2009: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2010: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2011: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2012: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2013: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2014: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2015: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2016: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2017: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2018: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2019: In QELM, logits are produced classically after quantum aggregation.
FACT 2020: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2021: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2022: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2023: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2024: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2025: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2026: In QELM, logits are produced classically after quantum aggregation.
FACT 2027: In QELM, logits are produced classically after quantum aggregation.
FACT 2028: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2029: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2030: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2031: In QELM, logits are produced classically after quantum aggregation.
FACT 2032: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2033: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2034: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2035: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2036: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2037: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2038: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2039: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2040: In QELM, logits are produced classically after quantum aggregation.
FACT 2041: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2042: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2043: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2044: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2045: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2046: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2047: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2048: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2049: In QELM, logits are produced classically after quantum aggregation.
FACT 2050: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2051: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2052: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2053: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2054: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2055: In QELM, logits are produced classically after quantum aggregation.
FACT 2056: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2057: In QELM, logits are produced classically after quantum aggregation.
FACT 2058: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2059: In QELM, logits are produced classically after quantum aggregation.
FACT 2060: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2061: In QELM, logits are produced classically after quantum aggregation.
FACT 2062: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2063: In QELM, logits are produced classically after quantum aggregation.
FACT 2064: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2065: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2066: In QELM, logits are produced classically after quantum aggregation.
FACT 2067: In QELM, logits are produced classically after quantum aggregation.
FACT 2068: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2069: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2070: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2071: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2072: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2073: In QELM, logits are produced classically after quantum aggregation.
FACT 2074: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2075: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2076: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2077: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2078: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2079: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2080: In QELM, logits are produced classically after quantum aggregation.
FACT 2081: In QELM, logits are produced classically after quantum aggregation.
FACT 2082: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2083: In QELM, logits are produced classically after quantum aggregation.
FACT 2084: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2085: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2086: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2087: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2088: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2089: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2090: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2091: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2092: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2093: In QELM, logits are produced classically after quantum aggregation.
FACT 2094: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2095: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2096: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2097: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2098: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2099: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2100: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2101: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2102: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2103: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2104: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2105: In QELM, logits are produced classically after quantum aggregation.
FACT 2106: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2107: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2108: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2109: In QELM, logits are produced classically after quantum aggregation.
FACT 2110: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2111: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2112: In QELM, logits are produced classically after quantum aggregation.
FACT 2113: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2114: In QELM, logits are produced classically after quantum aggregation.
FACT 2115: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2116: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2117: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2118: In QELM, logits are produced classically after quantum aggregation.
FACT 2119: In QELM, logits are produced classically after quantum aggregation.
FACT 2120: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2121: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2122: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2123: In QELM, logits are produced classically after quantum aggregation.
FACT 2124: In QELM, logits are produced classically after quantum aggregation.
FACT 2125: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2126: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2127: In QELM, logits are produced classically after quantum aggregation.
FACT 2128: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2129: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2130: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2131: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2132: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2133: In QELM, logits are produced classically after quantum aggregation.
FACT 2134: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2135: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2136: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2137: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2138: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2139: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2140: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2141: In QELM, logits are produced classically after quantum aggregation.
FACT 2142: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2143: In QELM, logits are produced classically after quantum aggregation.
FACT 2144: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2145: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2146: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2147: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2148: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2149: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2150: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2151: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2152: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2153: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2154: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2155: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2156: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2157: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2158: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2159: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2160: In QELM, logits are produced classically after quantum aggregation.
FACT 2161: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2162: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2163: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2164: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2165: In QELM, logits are produced classically after quantum aggregation.
FACT 2166: In QELM, logits are produced classically after quantum aggregation.
FACT 2167: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2168: In QELM, logits are produced classically after quantum aggregation.
FACT 2169: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2170: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2171: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2172: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2173: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2174: In QELM, logits are produced classically after quantum aggregation.
FACT 2175: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2176: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2177: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2178: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2179: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2180: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2181: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2182: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2183: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2184: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2185: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2186: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2187: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2188: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2189: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2190: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2191: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2192: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2193: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2194: In QELM, logits are produced classically after quantum aggregation.
FACT 2195: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2196: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2197: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2198: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2199: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2200: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2201: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2202: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2203: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2204: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2205: In QELM, logits are produced classically after quantum aggregation.
FACT 2206: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2207: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2208: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2209: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2210: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2211: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2212: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2213: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2214: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2215: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2216: In QELM, logits are produced classically after quantum aggregation.
FACT 2217: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2218: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2219: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2220: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2221: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2222: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2223: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2224: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2225: In QELM, logits are produced classically after quantum aggregation.
FACT 2226: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2227: In QELM, logits are produced classically after quantum aggregation.
FACT 2228: In QELM, logits are produced classically after quantum aggregation.
FACT 2229: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2230: In QELM, logits are produced classically after quantum aggregation.
FACT 2231: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2232: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2233: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2234: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2235: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2236: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2237: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2238: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2239: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2240: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2241: In QELM, logits are produced classically after quantum aggregation.
FACT 2242: In QELM, logits are produced classically after quantum aggregation.
FACT 2243: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2244: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2245: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2246: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2247: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2248: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2249: In QELM, logits are produced classically after quantum aggregation.
FACT 2250: In QELM, logits are produced classically after quantum aggregation.
FACT 2251: In QELM, logits are produced classically after quantum aggregation.
FACT 2252: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2253: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2254: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2255: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2256: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2257: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2258: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2259: In QELM, logits are produced classically after quantum aggregation.
FACT 2260: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2261: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2262: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2263: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2264: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2265: In QELM, logits are produced classically after quantum aggregation.
FACT 2266: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2267: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2268: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2269: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2270: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2271: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2272: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2273: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2274: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2275: In QELM, logits are produced classically after quantum aggregation.
FACT 2276: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2277: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2278: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2279: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2280: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2281: In QELM, logits are produced classically after quantum aggregation.
FACT 2282: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2283: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2284: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2285: In QELM, logits are produced classically after quantum aggregation.
FACT 2286: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2287: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2288: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2289: In QELM, logits are produced classically after quantum aggregation.
FACT 2290: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2291: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2292: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2293: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2294: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2295: In QELM, logits are produced classically after quantum aggregation.
FACT 2296: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2297: In QELM, logits are produced classically after quantum aggregation.
FACT 2298: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2299: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2300: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2301: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2302: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2303: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2304: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2305: In QELM, logits are produced classically after quantum aggregation.
FACT 2306: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2307: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2308: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2309: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2310: In QELM, logits are produced classically after quantum aggregation.
FACT 2311: In QELM, logits are produced classically after quantum aggregation.
FACT 2312: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2313: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2314: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2315: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2316: In QELM, logits are produced classically after quantum aggregation.
FACT 2317: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2318: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2319: In QELM, logits are produced classically after quantum aggregation.
FACT 2320: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2321: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2322: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2323: In QELM, logits are produced classically after quantum aggregation.
FACT 2324: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2325: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2326: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2327: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2328: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2329: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2330: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2331: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2332: In QELM, logits are produced classically after quantum aggregation.
FACT 2333: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2334: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2335: In QELM, logits are produced classically after quantum aggregation.
FACT 2336: In QELM, logits are produced classically after quantum aggregation.
FACT 2337: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2338: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2339: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2340: In QELM, logits are produced classically after quantum aggregation.
FACT 2341: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2342: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2343: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2344: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2345: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2346: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2347: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2348: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2349: In QELM, logits are produced classically after quantum aggregation.
FACT 2350: In QELM, logits are produced classically after quantum aggregation.
FACT 2351: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2352: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2353: In QELM, logits are produced classically after quantum aggregation.
FACT 2354: In QELM, logits are produced classically after quantum aggregation.
FACT 2355: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2356: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2357: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2358: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2359: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2360: In QELM, logits are produced classically after quantum aggregation.
FACT 2361: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2362: In QELM, logits are produced classically after quantum aggregation.
FACT 2363: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2364: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2365: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2366: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2367: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2368: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2369: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2370: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2371: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2372: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2373: In QELM, logits are produced classically after quantum aggregation.
FACT 2374: In QELM, logits are produced classically after quantum aggregation.
FACT 2375: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2376: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2377: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2378: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2379: In QELM, logits are produced classically after quantum aggregation.
FACT 2380: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2381: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2382: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2383: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2384: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2385: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2386: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2387: In QELM, logits are produced classically after quantum aggregation.
FACT 2388: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2389: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2390: In QELM, logits are produced classically after quantum aggregation.
FACT 2391: In QELM, logits are produced classically after quantum aggregation.
FACT 2392: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2393: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2394: In QELM, logits are produced classically after quantum aggregation.
FACT 2395: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2396: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2397: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2398: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2399: In QELM, logits are produced classically after quantum aggregation.
FACT 2400: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2401: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2402: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2403: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2404: In QELM, logits are produced classically after quantum aggregation.
FACT 2405: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2406: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2407: In QELM, logits are produced classically after quantum aggregation.
FACT 2408: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2409: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2410: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2411: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2412: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2413: In QELM, logits are produced classically after quantum aggregation.
FACT 2414: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2415: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2416: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2417: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2418: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2419: In QELM, logits are produced classically after quantum aggregation.
FACT 2420: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2421: In QELM, logits are produced classically after quantum aggregation.
FACT 2422: In QELM, logits are produced classically after quantum aggregation.
FACT 2423: In QELM, logits are produced classically after quantum aggregation.
FACT 2424: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2425: In QELM, logits are produced classically after quantum aggregation.
FACT 2426: In QELM, logits are produced classically after quantum aggregation.
FACT 2427: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2428: In QELM, logits are produced classically after quantum aggregation.
FACT 2429: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2430: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2431: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2432: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2433: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2434: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2435: In QELM, logits are produced classically after quantum aggregation.
FACT 2436: In QELM, logits are produced classically after quantum aggregation.
FACT 2437: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2438: In QELM, logits are produced classically after quantum aggregation.
FACT 2439: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2440: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2441: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2442: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2443: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2444: In QELM, logits are produced classically after quantum aggregation.
FACT 2445: In QELM, logits are produced classically after quantum aggregation.
FACT 2446: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2447: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2448: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2449: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2450: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2451: In QELM, logits are produced classically after quantum aggregation.
FACT 2452: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2453: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2454: In QELM, logits are produced classically after quantum aggregation.
FACT 2455: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2456: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2457: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2458: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2459: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2460: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2461: In QELM, logits are produced classically after quantum aggregation.
FACT 2462: In QELM, logits are produced classically after quantum aggregation.
FACT 2463: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2464: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2465: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2466: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2467: In QELM, logits are produced classically after quantum aggregation.
FACT 2468: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2469: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2470: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2471: In QELM, logits are produced classically after quantum aggregation.
FACT 2472: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2473: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2474: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2475: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2476: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2477: In QELM, logits are produced classically after quantum aggregation.
FACT 2478: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2479: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2480: In QELM, logits are produced classically after quantum aggregation.
FACT 2481: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2482: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2483: In QELM, logits are produced classically after quantum aggregation.
FACT 2484: In QELM, logits are produced classically after quantum aggregation.
FACT 2485: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2486: In QELM, logits are produced classically after quantum aggregation.
FACT 2487: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2488: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2489: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2490: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2491: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2492: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2493: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2494: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2495: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2496: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2497: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2498: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2499: In QELM, logits are produced classically after quantum aggregation.
FACT 2500: In QELM, logits are produced classically after quantum aggregation.
FACT 2501: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2502: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2503: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2504: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2505: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2506: In QELM, logits are produced classically after quantum aggregation.
FACT 2507: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2508: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2509: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2510: In QELM, logits are produced classically after quantum aggregation.
FACT 2511: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2512: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2513: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2514: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2515: In QELM, logits are produced classically after quantum aggregation.
FACT 2516: In QELM, logits are produced classically after quantum aggregation.
FACT 2517: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2518: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2519: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2520: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2521: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2522: In QELM, logits are produced classically after quantum aggregation.
FACT 2523: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2524: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2525: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2526: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2527: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2528: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2529: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2530: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2531: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2532: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2533: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2534: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2535: In QELM, logits are produced classically after quantum aggregation.
FACT 2536: In QELM, logits are produced classically after quantum aggregation.
FACT 2537: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2538: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2539: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2540: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2541: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2542: In QELM, logits are produced classically after quantum aggregation.
FACT 2543: In QELM, logits are produced classically after quantum aggregation.
FACT 2544: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2545: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2546: In QELM, logits are produced classically after quantum aggregation.
FACT 2547: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2548: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2549: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2550: In QELM, logits are produced classically after quantum aggregation.
FACT 2551: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2552: In QELM, logits are produced classically after quantum aggregation.
FACT 2553: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2554: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2555: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2556: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2557: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2558: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2559: In QELM, logits are produced classically after quantum aggregation.
FACT 2560: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2561: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2562: In QELM, logits are produced classically after quantum aggregation.
FACT 2563: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2564: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2565: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2566: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2567: In QELM, logits are produced classically after quantum aggregation.
FACT 2568: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2569: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2570: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2571: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2572: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2573: In QELM, logits are produced classically after quantum aggregation.
FACT 2574: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2575: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2576: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2577: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2578: In QELM, logits are produced classically after quantum aggregation.
FACT 2579: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2580: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2581: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2582: In QELM, logits are produced classically after quantum aggregation.
FACT 2583: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2584: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2585: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2586: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2587: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2588: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2589: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2590: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2591: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2592: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2593: In QELM, logits are produced classically after quantum aggregation.
FACT 2594: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2595: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2596: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2597: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2598: In QELM, logits are produced classically after quantum aggregation.
FACT 2599: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2600: In QELM, logits are produced classically after quantum aggregation.
FACT 2601: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2602: In QELM, logits are produced classically after quantum aggregation.
FACT 2603: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2604: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2605: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2606: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2607: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2608: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2609: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2610: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2611: In QELM, logits are produced classically after quantum aggregation.
FACT 2612: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2613: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2614: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2615: In QELM, logits are produced classically after quantum aggregation.
FACT 2616: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2617: In QELM, logits are produced classically after quantum aggregation.
FACT 2618: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2619: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2620: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2621: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2622: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2623: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2624: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2625: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2626: In QELM, logits are produced classically after quantum aggregation.
FACT 2627: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2628: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2629: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2630: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2631: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2632: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2633: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2634: In QELM, logits are produced classically after quantum aggregation.
FACT 2635: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2636: In QELM, logits are produced classically after quantum aggregation.
FACT 2637: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2638: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2639: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2640: In QELM, logits are produced classically after quantum aggregation.
FACT 2641: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2642: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2643: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2644: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2645: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2646: In QELM, logits are produced classically after quantum aggregation.
FACT 2647: In QELM, logits are produced classically after quantum aggregation.
FACT 2648: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2649: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2650: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2651: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2652: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2653: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2654: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2655: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2656: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2657: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2658: In QELM, logits are produced classically after quantum aggregation.
FACT 2659: In QELM, logits are produced classically after quantum aggregation.
FACT 2660: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2661: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2662: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2663: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2664: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2665: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2666: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2667: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2668: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2669: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2670: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2671: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2672: In QELM, logits are produced classically after quantum aggregation.
FACT 2673: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2674: In QELM, logits are produced classically after quantum aggregation.
FACT 2675: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2676: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2677: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2678: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2679: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2680: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2681: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2682: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2683: In QELM, logits are produced classically after quantum aggregation.
FACT 2684: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2685: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2686: In QELM, logits are produced classically after quantum aggregation.
FACT 2687: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2688: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2689: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2690: In QELM, logits are produced classically after quantum aggregation.
FACT 2691: In QELM, logits are produced classically after quantum aggregation.
FACT 2692: In QELM, logits are produced classically after quantum aggregation.
FACT 2693: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2694: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2695: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2696: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2697: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2698: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2699: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2700: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2701: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2702: In QELM, logits are produced classically after quantum aggregation.
FACT 2703: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2704: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2705: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2706: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2707: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2708: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2709: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2710: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2711: In QELM, logits are produced classically after quantum aggregation.
FACT 2712: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2713: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2714: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2715: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2716: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2717: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2718: In QELM, logits are produced classically after quantum aggregation.
FACT 2719: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2720: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2721: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2722: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2723: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2724: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2725: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2726: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2727: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2728: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2729: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2730: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2731: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2732: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2733: In QELM, logits are produced classically after quantum aggregation.
FACT 2734: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2735: In QELM, logits are produced classically after quantum aggregation.
FACT 2736: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2737: In QELM, logits are produced classically after quantum aggregation.
FACT 2738: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2739: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2740: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2741: In QELM, logits are produced classically after quantum aggregation.
FACT 2742: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2743: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2744: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2745: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2746: In QELM, logits are produced classically after quantum aggregation.
FACT 2747: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2748: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2749: In QELM, logits are produced classically after quantum aggregation.
FACT 2750: In QELM, logits are produced classically after quantum aggregation.
FACT 2751: In QELM, logits are produced classically after quantum aggregation.
FACT 2752: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2753: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2754: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2755: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2756: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2757: In QELM, logits are produced classically after quantum aggregation.
FACT 2758: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2759: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2760: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2761: In QELM, logits are produced classically after quantum aggregation.
FACT 2762: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2763: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2764: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2765: In QELM, logits are produced classically after quantum aggregation.
FACT 2766: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2767: In QELM, logits are produced classically after quantum aggregation.
FACT 2768: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2769: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2770: In QELM, logits are produced classically after quantum aggregation.
FACT 2771: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2772: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2773: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2774: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2775: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2776: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2777: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2778: In QELM, logits are produced classically after quantum aggregation.
FACT 2779: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2780: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2781: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2782: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2783: In QELM, logits are produced classically after quantum aggregation.
FACT 2784: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2785: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2786: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2787: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2788: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2789: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2790: In QELM, logits are produced classically after quantum aggregation.
FACT 2791: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2792: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2793: In QELM, logits are produced classically after quantum aggregation.
FACT 2794: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2795: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2796: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2797: In QELM, logits are produced classically after quantum aggregation.
FACT 2798: In QELM, logits are produced classically after quantum aggregation.
FACT 2799: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2800: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2801: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2802: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2803: In QELM, logits are produced classically after quantum aggregation.
FACT 2804: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2805: In QELM, logits are produced classically after quantum aggregation.
FACT 2806: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2807: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2808: In QELM, logits are produced classically after quantum aggregation.
FACT 2809: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2810: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2811: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2812: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2813: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2814: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2815: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2816: In QELM, logits are produced classically after quantum aggregation.
FACT 2817: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2818: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2819: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2820: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2821: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2822: In QELM, logits are produced classically after quantum aggregation.
FACT 2823: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2824: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2825: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2826: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2827: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2828: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2829: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2830: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2831: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2832: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2833: In QELM, logits are produced classically after quantum aggregation.
FACT 2834: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2835: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2836: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2837: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2838: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2839: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2840: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2841: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2842: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2843: In QELM, logits are produced classically after quantum aggregation.
FACT 2844: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2845: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2846: In QELM, logits are produced classically after quantum aggregation.
FACT 2847: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2848: In QELM, logits are produced classically after quantum aggregation.
FACT 2849: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2850: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2851: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2852: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2853: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2854: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2855: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2856: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2857: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2858: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2859: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2860: In QELM, logits are produced classically after quantum aggregation.
FACT 2861: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2862: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2863: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2864: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2865: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2866: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2867: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2868: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2869: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2870: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2871: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2872: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2873: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2874: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2875: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2876: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2877: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2878: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2879: In QELM, logits are produced classically after quantum aggregation.
FACT 2880: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2881: In QELM, logits are produced classically after quantum aggregation.
FACT 2882: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2883: In QELM, logits are produced classically after quantum aggregation.
FACT 2884: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2885: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2886: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2887: In QELM, logits are produced classically after quantum aggregation.
FACT 2888: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2889: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2890: In QELM, logits are produced classically after quantum aggregation.
FACT 2891: In QELM, logits are produced classically after quantum aggregation.
FACT 2892: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2893: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2894: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2895: In QELM, logits are produced classically after quantum aggregation.
FACT 2896: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2897: In QELM, logits are produced classically after quantum aggregation.
FACT 2898: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2899: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2900: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2901: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2902: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2903: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2904: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2905: In QELM, logits are produced classically after quantum aggregation.
FACT 2906: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2907: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2908: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2909: In QELM, logits are produced classically after quantum aggregation.
FACT 2910: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2911: In QELM, logits are produced classically after quantum aggregation.
FACT 2912: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2913: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2914: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2915: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2916: In QELM, logits are produced classically after quantum aggregation.
FACT 2917: In QELM, logits are produced classically after quantum aggregation.
FACT 2918: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2919: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2920: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2921: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2922: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2923: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2924: In QELM, logits are produced classically after quantum aggregation.
FACT 2925: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2926: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2927: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2928: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2929: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2930: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2931: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2932: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2933: In QELM, logits are produced classically after quantum aggregation.
FACT 2934: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2935: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2936: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2937: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2938: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2939: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2940: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2941: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2942: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2943: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2944: In QELM, logits are produced classically after quantum aggregation.
FACT 2945: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2946: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2947: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2948: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2949: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2950: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2951: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2952: In QELM, logits are produced classically after quantum aggregation.
FACT 2953: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2954: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2955: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2956: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2957: In QELM, logits are produced classically after quantum aggregation.
FACT 2958: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2959: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2960: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2961: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2962: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2963: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2964: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2965: In QELM, logits are produced classically after quantum aggregation.
FACT 2966: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2967: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2968: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2969: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2970: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2971: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2972: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2973: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2974: In QELM, logits are produced classically after quantum aggregation.
FACT 2975: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2976: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2977: In QELM, logits are produced classically after quantum aggregation.
FACT 2978: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2979: In QELM, logits are produced classically after quantum aggregation.
FACT 2980: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2981: In QELM, logits are produced classically after quantum aggregation.
FACT 2982: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2983: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2984: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2985: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2986: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2987: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2988: In QELM, logits are produced classically after quantum aggregation.
FACT 2989: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2990: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2991: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2992: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2993: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 2994: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2995: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2996: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 2997: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 2998: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 2999: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3000: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3001: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3002: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3003: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3004: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3005: In QELM, logits are produced classically after quantum aggregation.
FACT 3006: In QELM, logits are produced classically after quantum aggregation.
FACT 3007: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3008: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3009: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3010: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3011: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3012: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3013: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3014: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3015: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3016: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3017: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3018: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3019: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3020: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3021: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3022: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3023: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3024: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3025: In QELM, logits are produced classically after quantum aggregation.
FACT 3026: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3027: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3028: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3029: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3030: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3031: In QELM, logits are produced classically after quantum aggregation.
FACT 3032: In QELM, logits are produced classically after quantum aggregation.
FACT 3033: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3034: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3035: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3036: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3037: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3038: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3039: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3040: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3041: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3042: In QELM, logits are produced classically after quantum aggregation.
FACT 3043: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3044: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3045: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3046: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3047: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3048: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3049: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3050: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3051: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3052: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3053: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3054: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3055: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3056: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3057: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3058: In QELM, logits are produced classically after quantum aggregation.
FACT 3059: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3060: In QELM, logits are produced classically after quantum aggregation.
FACT 3061: In QELM, logits are produced classically after quantum aggregation.
FACT 3062: In QELM, logits are produced classically after quantum aggregation.
FACT 3063: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3064: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3065: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3066: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3067: In QELM, logits are produced classically after quantum aggregation.
FACT 3068: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3069: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3070: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3071: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3072: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3073: In QELM, logits are produced classically after quantum aggregation.
FACT 3074: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3075: In QELM, logits are produced classically after quantum aggregation.
FACT 3076: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3077: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3078: In QELM, logits are produced classically after quantum aggregation.
FACT 3079: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3080: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3081: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3082: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3083: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3084: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3085: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3086: In QELM, logits are produced classically after quantum aggregation.
FACT 3087: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3088: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3089: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3090: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3091: In QELM, logits are produced classically after quantum aggregation.
FACT 3092: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3093: In QELM, logits are produced classically after quantum aggregation.
FACT 3094: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3095: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3096: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3097: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3098: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3099: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3100: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3101: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3102: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3103: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3104: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3105: In QELM, logits are produced classically after quantum aggregation.
FACT 3106: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3107: In QELM, logits are produced classically after quantum aggregation.
FACT 3108: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3109: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3110: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3111: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3112: In QELM, logits are produced classically after quantum aggregation.
FACT 3113: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3114: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3115: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3116: In QELM, logits are produced classically after quantum aggregation.
FACT 3117: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3118: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3119: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3120: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3121: In QELM, logits are produced classically after quantum aggregation.
FACT 3122: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3123: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3124: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3125: In QELM, logits are produced classically after quantum aggregation.
FACT 3126: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3127: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3128: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3129: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3130: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3131: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3132: In QELM, logits are produced classically after quantum aggregation.
FACT 3133: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3134: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3135: In QELM, logits are produced classically after quantum aggregation.
FACT 3136: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3137: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3138: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3139: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3140: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3141: In QELM, logits are produced classically after quantum aggregation.
FACT 3142: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3143: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3144: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3145: In QELM, logits are produced classically after quantum aggregation.
FACT 3146: In QELM, logits are produced classically after quantum aggregation.
FACT 3147: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3148: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3149: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3150: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3151: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3152: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3153: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3154: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3155: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3156: In QELM, logits are produced classically after quantum aggregation.
FACT 3157: In QELM, logits are produced classically after quantum aggregation.
FACT 3158: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3159: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3160: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3161: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3162: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3163: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3164: In QELM, logits are produced classically after quantum aggregation.
FACT 3165: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3166: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3167: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3168: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3169: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3170: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3171: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3172: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3173: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3174: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3175: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3176: In QELM, logits are produced classically after quantum aggregation.
FACT 3177: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3178: In QELM, logits are produced classically after quantum aggregation.
FACT 3179: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3180: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3181: In QELM, logits are produced classically after quantum aggregation.
FACT 3182: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3183: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3184: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3185: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3186: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3187: In QELM, logits are produced classically after quantum aggregation.
FACT 3188: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3189: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3190: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3191: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3192: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3193: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3194: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3195: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3196: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3197: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3198: In QELM, logits are produced classically after quantum aggregation.
FACT 3199: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3200: In QELM, logits are produced classically after quantum aggregation.
FACT 3201: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3202: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3203: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3204: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3205: In QELM, logits are produced classically after quantum aggregation.
FACT 3206: In QELM, logits are produced classically after quantum aggregation.
FACT 3207: In QELM, logits are produced classically after quantum aggregation.
FACT 3208: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3209: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3210: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3211: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3212: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3213: In QELM, logits are produced classically after quantum aggregation.
FACT 3214: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3215: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3216: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3217: In QELM, logits are produced classically after quantum aggregation.
FACT 3218: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3219: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3220: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3221: In QELM, logits are produced classically after quantum aggregation.
FACT 3222: In QELM, logits are produced classically after quantum aggregation.
FACT 3223: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3224: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3225: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3226: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3227: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3228: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3229: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3230: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3231: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3232: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3233: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3234: In QELM, logits are produced classically after quantum aggregation.
FACT 3235: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3236: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3237: In QELM, logits are produced classically after quantum aggregation.
FACT 3238: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3239: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3240: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3241: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3242: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3243: In QELM, logits are produced classically after quantum aggregation.
FACT 3244: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3245: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3246: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3247: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3248: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3249: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3250: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3251: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3252: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3253: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3254: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3255: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3256: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3257: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3258: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3259: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3260: In QELM, logits are produced classically after quantum aggregation.
FACT 3261: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3262: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3263: In QELM, logits are produced classically after quantum aggregation.
FACT 3264: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3265: In QELM, logits are produced classically after quantum aggregation.
FACT 3266: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3267: In QELM, logits are produced classically after quantum aggregation.
FACT 3268: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3269: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3270: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3271: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3272: In QELM, logits are produced classically after quantum aggregation.
FACT 3273: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3274: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3275: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3276: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3277: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3278: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3279: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3280: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3281: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3282: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3283: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3284: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3285: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3286: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3287: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3288: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3289: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3290: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3291: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3292: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3293: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3294: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3295: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3296: In QELM, logits are produced classically after quantum aggregation.
FACT 3297: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3298: In QELM, logits are produced classically after quantum aggregation.
FACT 3299: In QELM, logits are produced classically after quantum aggregation.
FACT 3300: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3301: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3302: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3303: In QELM, logits are produced classically after quantum aggregation.
FACT 3304: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3305: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3306: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3307: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3308: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3309: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3310: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3311: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3312: In QELM, logits are produced classically after quantum aggregation.
FACT 3313: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3314: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3315: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3316: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3317: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3318: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3319: In QELM, logits are produced classically after quantum aggregation.
FACT 3320: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3321: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3322: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3323: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3324: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3325: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3326: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3327: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3328: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3329: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3330: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3331: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3332: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3333: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3334: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3335: In QELM, logits are produced classically after quantum aggregation.
FACT 3336: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3337: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3338: In QELM, logits are produced classically after quantum aggregation.
FACT 3339: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3340: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3341: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3342: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3343: In QELM, logits are produced classically after quantum aggregation.
FACT 3344: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3345: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3346: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3347: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3348: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3349: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3350: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3351: In QELM, logits are produced classically after quantum aggregation.
FACT 3352: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3353: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3354: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3355: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3356: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3357: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3358: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3359: In QELM, logits are produced classically after quantum aggregation.
FACT 3360: In QELM, logits are produced classically after quantum aggregation.
FACT 3361: In QELM, logits are produced classically after quantum aggregation.
FACT 3362: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3363: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3364: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3365: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3366: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3367: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3368: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3369: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3370: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3371: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3372: In QELM, logits are produced classically after quantum aggregation.
FACT 3373: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3374: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3375: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3376: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3377: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3378: In QELM, logits are produced classically after quantum aggregation.
FACT 3379: In QELM, logits are produced classically after quantum aggregation.
FACT 3380: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3381: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3382: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3383: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3384: In QELM, logits are produced classically after quantum aggregation.
FACT 3385: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3386: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3387: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3388: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3389: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3390: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3391: In QELM, logits are produced classically after quantum aggregation.
FACT 3392: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3393: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3394: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3395: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3396: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3397: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3398: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3399: In QELM, logits are produced classically after quantum aggregation.
FACT 3400: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3401: In QELM, logits are produced classically after quantum aggregation.
FACT 3402: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3403: In QELM, logits are produced classically after quantum aggregation.
FACT 3404: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3405: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3406: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3407: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3408: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3409: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3410: In QELM, logits are produced classically after quantum aggregation.
FACT 3411: In QELM, logits are produced classically after quantum aggregation.
FACT 3412: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3413: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3414: In QELM, logits are produced classically after quantum aggregation.
FACT 3415: In QELM, logits are produced classically after quantum aggregation.
FACT 3416: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3417: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3418: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3419: In QELM, logits are produced classically after quantum aggregation.
FACT 3420: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3421: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3422: In QELM, logits are produced classically after quantum aggregation.
FACT 3423: In QELM, logits are produced classically after quantum aggregation.
FACT 3424: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3425: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3426: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3427: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3428: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3429: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3430: In QELM, logits are produced classically after quantum aggregation.
FACT 3431: In QELM, logits are produced classically after quantum aggregation.
FACT 3432: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3433: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3434: In QELM, logits are produced classically after quantum aggregation.
FACT 3435: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3436: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3437: In QELM, logits are produced classically after quantum aggregation.
FACT 3438: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3439: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3440: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3441: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3442: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3443: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3444: In QELM, logits are produced classically after quantum aggregation.
FACT 3445: In QELM, logits are produced classically after quantum aggregation.
FACT 3446: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3447: In QELM, logits are produced classically after quantum aggregation.
FACT 3448: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3449: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3450: In QELM, logits are produced classically after quantum aggregation.
FACT 3451: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3452: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3453: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3454: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3455: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3456: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3457: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3458: In QELM, logits are produced classically after quantum aggregation.
FACT 3459: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3460: In QELM, logits are produced classically after quantum aggregation.
FACT 3461: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3462: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3463: In QELM, logits are produced classically after quantum aggregation.
FACT 3464: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3465: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3466: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3467: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3468: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3469: In QELM, logits are produced classically after quantum aggregation.
FACT 3470: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3471: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3472: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3473: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3474: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3475: In QELM, logits are produced classically after quantum aggregation.
FACT 3476: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3477: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3478: In QELM, logits are produced classically after quantum aggregation.
FACT 3479: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3480: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3481: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3482: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3483: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3484: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3485: In QELM, logits are produced classically after quantum aggregation.
FACT 3486: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3487: In QELM, logits are produced classically after quantum aggregation.
FACT 3488: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3489: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3490: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3491: In QELM, logits are produced classically after quantum aggregation.
FACT 3492: In QELM, logits are produced classically after quantum aggregation.
FACT 3493: In QELM, logits are produced classically after quantum aggregation.
FACT 3494: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3495: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3496: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3497: In QELM, logits are produced classically after quantum aggregation.
FACT 3498: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3499: In QELM, logits are produced classically after quantum aggregation.
FACT 3500: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3501: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3502: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3503: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3504: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3505: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3506: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3507: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3508: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3509: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3510: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3511: In QELM, logits are produced classically after quantum aggregation.
FACT 3512: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3513: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3514: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3515: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3516: In QELM, logits are produced classically after quantum aggregation.
FACT 3517: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3518: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3519: In QELM, logits are produced classically after quantum aggregation.
FACT 3520: In QELM, logits are produced classically after quantum aggregation.
FACT 3521: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3522: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3523: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3524: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3525: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3526: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3527: In QELM, logits are produced classically after quantum aggregation.
FACT 3528: In QELM, logits are produced classically after quantum aggregation.
FACT 3529: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3530: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3531: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3532: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3533: In QELM, logits are produced classically after quantum aggregation.
FACT 3534: In QELM, logits are produced classically after quantum aggregation.
FACT 3535: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3536: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3537: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3538: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3539: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3540: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3541: In QELM, logits are produced classically after quantum aggregation.
FACT 3542: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3543: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3544: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3545: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3546: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3547: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3548: In QELM, logits are produced classically after quantum aggregation.
FACT 3549: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3550: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3551: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3552: In QELM, logits are produced classically after quantum aggregation.
FACT 3553: In QELM, logits are produced classically after quantum aggregation.
FACT 3554: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3555: In QELM, logits are produced classically after quantum aggregation.
FACT 3556: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3557: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3558: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3559: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3560: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3561: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3562: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3563: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3564: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3565: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3566: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3567: In QELM, logits are produced classically after quantum aggregation.
FACT 3568: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3569: In QELM, logits are produced classically after quantum aggregation.
FACT 3570: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3571: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3572: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3573: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3574: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3575: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3576: In QELM, logits are produced classically after quantum aggregation.
FACT 3577: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3578: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3579: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3580: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3581: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3582: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3583: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3584: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3585: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3586: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3587: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3588: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3589: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3590: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3591: In QELM, logits are produced classically after quantum aggregation.
FACT 3592: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3593: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3594: In QELM, logits are produced classically after quantum aggregation.
FACT 3595: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3596: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3597: In QELM, logits are produced classically after quantum aggregation.
FACT 3598: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3599: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3600: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3601: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3602: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3603: In QELM, logits are produced classically after quantum aggregation.
FACT 3604: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3605: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3606: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3607: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3608: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3609: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3610: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3611: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3612: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3613: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3614: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3615: In QELM, logits are produced classically after quantum aggregation.
FACT 3616: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3617: In QELM, logits are produced classically after quantum aggregation.
FACT 3618: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3619: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3620: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3621: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3622: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3623: In QELM, logits are produced classically after quantum aggregation.
FACT 3624: In QELM, logits are produced classically after quantum aggregation.
FACT 3625: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3626: In QELM, logits are produced classically after quantum aggregation.
FACT 3627: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3628: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3629: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3630: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3631: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3632: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3633: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3634: In QELM, logits are produced classically after quantum aggregation.
FACT 3635: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3636: In QELM, logits are produced classically after quantum aggregation.
FACT 3637: In QELM, logits are produced classically after quantum aggregation.
FACT 3638: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3639: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3640: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3641: In QELM, logits are produced classically after quantum aggregation.
FACT 3642: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3643: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3644: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3645: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3646: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3647: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3648: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3649: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3650: In QELM, logits are produced classically after quantum aggregation.
FACT 3651: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3652: In QELM, logits are produced classically after quantum aggregation.
FACT 3653: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3654: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3655: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3656: In QELM, logits are produced classically after quantum aggregation.
FACT 3657: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3658: In QELM, logits are produced classically after quantum aggregation.
FACT 3659: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3660: In QELM, logits are produced classically after quantum aggregation.
FACT 3661: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3662: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3663: In QELM, logits are produced classically after quantum aggregation.
FACT 3664: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3665: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3666: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3667: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3668: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3669: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3670: In QELM, logits are produced classically after quantum aggregation.
FACT 3671: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3672: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3673: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3674: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3675: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3676: In QELM, logits are produced classically after quantum aggregation.
FACT 3677: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3678: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3679: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3680: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3681: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3682: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3683: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3684: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3685: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3686: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3687: In QELM, logits are produced classically after quantum aggregation.
FACT 3688: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3689: In QELM, logits are produced classically after quantum aggregation.
FACT 3690: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3691: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3692: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3693: In QELM, logits are produced classically after quantum aggregation.
FACT 3694: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3695: In QELM, logits are produced classically after quantum aggregation.
FACT 3696: In QELM, logits are produced classically after quantum aggregation.
FACT 3697: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3698: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3699: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3700: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3701: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3702: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3703: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3704: In QELM, logits are produced classically after quantum aggregation.
FACT 3705: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3706: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3707: In QELM, logits are produced classically after quantum aggregation.
FACT 3708: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3709: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3710: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3711: In QELM, logits are produced classically after quantum aggregation.
FACT 3712: In QELM, logits are produced classically after quantum aggregation.
FACT 3713: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3714: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3715: In QELM, logits are produced classically after quantum aggregation.
FACT 3716: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3717: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3718: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3719: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3720: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3721: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3722: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3723: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3724: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3725: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3726: In QELM, logits are produced classically after quantum aggregation.
FACT 3727: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3728: In QELM, logits are produced classically after quantum aggregation.
FACT 3729: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3730: In QELM, logits are produced classically after quantum aggregation.
FACT 3731: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3732: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3733: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3734: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3735: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3736: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3737: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3738: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3739: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3740: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3741: In QELM, logits are produced classically after quantum aggregation.
FACT 3742: In QELM, logits are produced classically after quantum aggregation.
FACT 3743: In QELM, logits are produced classically after quantum aggregation.
FACT 3744: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3745: In QELM, logits are produced classically after quantum aggregation.
FACT 3746: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3747: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3748: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3749: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3750: In QELM, logits are produced classically after quantum aggregation.
FACT 3751: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3752: In QELM, logits are produced classically after quantum aggregation.
FACT 3753: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3754: In QELM, logits are produced classically after quantum aggregation.
FACT 3755: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3756: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3757: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3758: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3759: In QELM, logits are produced classically after quantum aggregation.
FACT 3760: In QELM, logits are produced classically after quantum aggregation.
FACT 3761: In QELM, logits are produced classically after quantum aggregation.
FACT 3762: In QELM, logits are produced classically after quantum aggregation.
FACT 3763: In QELM, logits are produced classically after quantum aggregation.
FACT 3764: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3765: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3766: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3767: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3768: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3769: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3770: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3771: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3772: In QELM, logits are produced classically after quantum aggregation.
FACT 3773: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3774: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3775: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3776: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3777: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3778: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3779: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3780: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3781: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3782: In QELM, logits are produced classically after quantum aggregation.
FACT 3783: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3784: In QELM, logits are produced classically after quantum aggregation.
FACT 3785: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3786: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3787: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3788: In QELM, logits are produced classically after quantum aggregation.
FACT 3789: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3790: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3791: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3792: In QELM, logits are produced classically after quantum aggregation.
FACT 3793: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3794: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3795: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3796: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3797: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3798: In QELM, logits are produced classically after quantum aggregation.
FACT 3799: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3800: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3801: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3802: In QELM, logits are produced classically after quantum aggregation.
FACT 3803: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3804: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3805: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3806: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3807: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3808: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3809: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3810: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3811: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3812: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3813: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3814: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3815: In QELM, logits are produced classically after quantum aggregation.
FACT 3816: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3817: In QELM, logits are produced classically after quantum aggregation.
FACT 3818: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3819: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3820: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3821: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3822: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3823: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3824: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3825: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3826: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3827: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3828: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3829: In QELM, logits are produced classically after quantum aggregation.
FACT 3830: In QELM, logits are produced classically after quantum aggregation.
FACT 3831: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3832: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3833: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3834: In QELM, logits are produced classically after quantum aggregation.
FACT 3835: In QELM, logits are produced classically after quantum aggregation.
FACT 3836: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3837: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3838: In QELM, logits are produced classically after quantum aggregation.
FACT 3839: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3840: In QELM, logits are produced classically after quantum aggregation.
FACT 3841: In QELM, logits are produced classically after quantum aggregation.
FACT 3842: In QELM, logits are produced classically after quantum aggregation.
FACT 3843: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3844: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3845: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3846: In QELM, logits are produced classically after quantum aggregation.
FACT 3847: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3848: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3849: In QELM, logits are produced classically after quantum aggregation.
FACT 3850: In QELM, logits are produced classically after quantum aggregation.
FACT 3851: In QELM, logits are produced classically after quantum aggregation.
FACT 3852: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3853: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3854: In QELM, logits are produced classically after quantum aggregation.
FACT 3855: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3856: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3857: In QELM, logits are produced classically after quantum aggregation.
FACT 3858: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3859: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3860: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3861: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3862: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3863: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3864: In QELM, logits are produced classically after quantum aggregation.
FACT 3865: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3866: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3867: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3868: In QELM, logits are produced classically after quantum aggregation.
FACT 3869: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3870: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3871: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3872: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3873: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3874: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3875: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3876: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3877: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3878: In QELM, logits are produced classically after quantum aggregation.
FACT 3879: In QELM, logits are produced classically after quantum aggregation.
FACT 3880: In QELM, logits are produced classically after quantum aggregation.
FACT 3881: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3882: In QELM, logits are produced classically after quantum aggregation.
FACT 3883: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3884: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3885: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3886: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3887: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3888: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3889: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3890: In QELM, logits are produced classically after quantum aggregation.
FACT 3891: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3892: In QELM, logits are produced classically after quantum aggregation.
FACT 3893: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3894: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3895: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3896: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3897: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3898: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3899: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3900: In QELM, logits are produced classically after quantum aggregation.
FACT 3901: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3902: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3903: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3904: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3905: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3906: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3907: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3908: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3909: In QELM, logits are produced classically after quantum aggregation.
FACT 3910: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3911: In QELM, logits are produced classically after quantum aggregation.
FACT 3912: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3913: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3914: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3915: In QELM, logits are produced classically after quantum aggregation.
FACT 3916: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3917: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3918: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3919: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3920: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3921: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3922: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3923: In QELM, logits are produced classically after quantum aggregation.
FACT 3924: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3925: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3926: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3927: In QELM, logits are produced classically after quantum aggregation.
FACT 3928: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3929: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3930: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3931: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3932: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3933: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3934: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3935: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3936: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3937: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3938: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3939: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3940: In QELM, logits are produced classically after quantum aggregation.
FACT 3941: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3942: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3943: In QELM, logits are produced classically after quantum aggregation.
FACT 3944: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3945: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3946: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3947: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3948: In QELM, logits are produced classically after quantum aggregation.
FACT 3949: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3950: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3951: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3952: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3953: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3954: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3955: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3956: In QELM, logits are produced classically after quantum aggregation.
FACT 3957: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3958: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3959: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3960: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3961: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3962: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3963: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3964: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3965: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3966: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3967: In QELM, logits are produced classically after quantum aggregation.
FACT 3968: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3969: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3970: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3971: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3972: In QELM, logits are produced classically after quantum aggregation.
FACT 3973: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3974: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3975: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3976: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3977: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3978: In QELM, logits are produced classically after quantum aggregation.
FACT 3979: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3980: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 3981: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3982: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3983: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3984: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3985: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3986: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3987: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3988: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3989: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3990: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3991: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3992: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 3993: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3994: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3995: In QELM, logits are produced classically after quantum aggregation.
FACT 3996: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3997: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 3998: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 3999: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4000: In QELM, logits are produced classically after quantum aggregation.
FACT 4001: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4002: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4003: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4004: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4005: In QELM, logits are produced classically after quantum aggregation.
FACT 4006: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4007: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4008: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4009: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4010: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4011: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4012: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4013: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4014: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4015: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4016: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4017: In QELM, logits are produced classically after quantum aggregation.
FACT 4018: In QELM, logits are produced classically after quantum aggregation.
FACT 4019: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4020: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4021: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4022: In QELM, logits are produced classically after quantum aggregation.
FACT 4023: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4024: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4025: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4026: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4027: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4028: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4029: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4030: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4031: In QELM, logits are produced classically after quantum aggregation.
FACT 4032: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4033: In QELM, logits are produced classically after quantum aggregation.
FACT 4034: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4035: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4036: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4037: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4038: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4039: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4040: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4041: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4042: In QELM, logits are produced classically after quantum aggregation.
FACT 4043: In QELM, logits are produced classically after quantum aggregation.
FACT 4044: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4045: In QELM, logits are produced classically after quantum aggregation.
FACT 4046: In QELM, logits are produced classically after quantum aggregation.
FACT 4047: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4048: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4049: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4050: In QELM, logits are produced classically after quantum aggregation.
FACT 4051: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4052: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4053: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4054: In QELM, logits are produced classically after quantum aggregation.
FACT 4055: In QELM, logits are produced classically after quantum aggregation.
FACT 4056: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4057: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4058: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4059: In QELM, logits are produced classically after quantum aggregation.
FACT 4060: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4061: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4062: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4063: In QELM, logits are produced classically after quantum aggregation.
FACT 4064: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4065: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4066: In QELM, logits are produced classically after quantum aggregation.
FACT 4067: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4068: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4069: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4070: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4071: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4072: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4073: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4074: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4075: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4076: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4077: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4078: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4079: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4080: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4081: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4082: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4083: In QELM, logits are produced classically after quantum aggregation.
FACT 4084: In QELM, logits are produced classically after quantum aggregation.
FACT 4085: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4086: In QELM, logits are produced classically after quantum aggregation.
FACT 4087: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4088: In QELM, logits are produced classically after quantum aggregation.
FACT 4089: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4090: In QELM, logits are produced classically after quantum aggregation.
FACT 4091: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4092: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4093: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4094: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4095: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4096: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4097: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4098: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4099: In QELM, logits are produced classically after quantum aggregation.
FACT 4100: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4101: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4102: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4103: In QELM, logits are produced classically after quantum aggregation.
FACT 4104: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4105: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4106: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4107: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4108: In QELM, logits are produced classically after quantum aggregation.
FACT 4109: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4110: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4111: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4112: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4113: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4114: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4115: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4116: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4117: In QELM, logits are produced classically after quantum aggregation.
FACT 4118: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4119: In QELM, logits are produced classically after quantum aggregation.
FACT 4120: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4121: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4122: In QELM, logits are produced classically after quantum aggregation.
FACT 4123: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4124: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4125: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4126: In QELM, logits are produced classically after quantum aggregation.
FACT 4127: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4128: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4129: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4130: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4131: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4132: In QELM, logits are produced classically after quantum aggregation.
FACT 4133: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4134: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4135: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4136: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4137: In QELM, logits are produced classically after quantum aggregation.
FACT 4138: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4139: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4140: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4141: In QELM, logits are produced classically after quantum aggregation.
FACT 4142: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4143: In QELM, logits are produced classically after quantum aggregation.
FACT 4144: In QELM, logits are produced classically after quantum aggregation.
FACT 4145: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4146: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4147: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4148: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4149: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4150: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4151: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4152: In QELM, logits are produced classically after quantum aggregation.
FACT 4153: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4154: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4155: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4156: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4157: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4158: In QELM, logits are produced classically after quantum aggregation.
FACT 4159: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4160: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4161: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4162: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4163: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4164: In QELM, logits are produced classically after quantum aggregation.
FACT 4165: In QELM, logits are produced classically after quantum aggregation.
FACT 4166: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4167: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4168: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4169: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4170: In QELM, logits are produced classically after quantum aggregation.
FACT 4171: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4172: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4173: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4174: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4175: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4176: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4177: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4178: In QELM, logits are produced classically after quantum aggregation.
FACT 4179: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4180: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4181: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4182: In QELM, logits are produced classically after quantum aggregation.
FACT 4183: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4184: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4185: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4186: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4187: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4188: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4189: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4190: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4191: In QELM, logits are produced classically after quantum aggregation.
FACT 4192: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4193: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4194: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4195: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4196: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4197: In QELM, logits are produced classically after quantum aggregation.
FACT 4198: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4199: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4200: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4201: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4202: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4203: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4204: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4205: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4206: In QELM, logits are produced classically after quantum aggregation.
FACT 4207: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4208: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4209: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4210: In QELM, logits are produced classically after quantum aggregation.
FACT 4211: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4212: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4213: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4214: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4215: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4216: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4217: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4218: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4219: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4220: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4221: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4222: In QELM, logits are produced classically after quantum aggregation.
FACT 4223: In QELM, logits are produced classically after quantum aggregation.
FACT 4224: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4225: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4226: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4227: In QELM, logits are produced classically after quantum aggregation.
FACT 4228: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4229: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4230: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4231: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4232: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4233: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4234: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4235: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4236: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4237: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4238: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4239: In QELM, logits are produced classically after quantum aggregation.
FACT 4240: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4241: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4242: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4243: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4244: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4245: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4246: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4247: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4248: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4249: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4250: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4251: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4252: In QELM, logits are produced classically after quantum aggregation.
FACT 4253: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4254: In QELM, logits are produced classically after quantum aggregation.
FACT 4255: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4256: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4257: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4258: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4259: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4260: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4261: In QELM, logits are produced classically after quantum aggregation.
FACT 4262: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4263: In QELM, logits are produced classically after quantum aggregation.
FACT 4264: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4265: In QELM, logits are produced classically after quantum aggregation.
FACT 4266: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4267: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4268: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4269: In QELM, logits are produced classically after quantum aggregation.
FACT 4270: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4271: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4272: In QELM, logits are produced classically after quantum aggregation.
FACT 4273: In QELM, logits are produced classically after quantum aggregation.
FACT 4274: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4275: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4276: In QELM, logits are produced classically after quantum aggregation.
FACT 4277: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4278: In QELM, logits are produced classically after quantum aggregation.
FACT 4279: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4280: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4281: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4282: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4283: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4284: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4285: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4286: In QELM, logits are produced classically after quantum aggregation.
FACT 4287: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4288: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4289: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4290: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4291: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4292: In QELM, logits are produced classically after quantum aggregation.
FACT 4293: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4294: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4295: In QELM, logits are produced classically after quantum aggregation.
FACT 4296: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4297: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4298: In QELM, logits are produced classically after quantum aggregation.
FACT 4299: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4300: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4301: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4302: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4303: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4304: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4305: In QELM, logits are produced classically after quantum aggregation.
FACT 4306: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4307: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4308: In QELM, logits are produced classically after quantum aggregation.
FACT 4309: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4310: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4311: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4312: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4313: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4314: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4315: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4316: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4317: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4318: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4319: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4320: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4321: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4322: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4323: In QELM, logits are produced classically after quantum aggregation.
FACT 4324: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4325: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4326: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4327: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4328: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4329: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4330: In QELM, logits are produced classically after quantum aggregation.
FACT 4331: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4332: In QELM, logits are produced classically after quantum aggregation.
FACT 4333: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4334: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4335: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4336: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4337: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4338: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4339: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4340: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4341: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4342: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4343: In QELM, logits are produced classically after quantum aggregation.
FACT 4344: In QELM, logits are produced classically after quantum aggregation.
FACT 4345: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4346: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4347: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4348: In QELM, logits are produced classically after quantum aggregation.
FACT 4349: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4350: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4351: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4352: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4353: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4354: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4355: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4356: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4357: In QELM, logits are produced classically after quantum aggregation.
FACT 4358: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4359: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4360: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4361: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4362: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4363: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4364: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4365: In QELM, logits are produced classically after quantum aggregation.
FACT 4366: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4367: In QELM, logits are produced classically after quantum aggregation.
FACT 4368: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4369: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4370: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4371: In QELM, logits are produced classically after quantum aggregation.
FACT 4372: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4373: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4374: In QELM, logits are produced classically after quantum aggregation.
FACT 4375: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4376: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4377: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4378: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4379: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4380: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4381: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4382: In QELM, logits are produced classically after quantum aggregation.
FACT 4383: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4384: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4385: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4386: In QELM, logits are produced classically after quantum aggregation.
FACT 4387: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4388: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4389: In QELM, logits are produced classically after quantum aggregation.
FACT 4390: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4391: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4392: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4393: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4394: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4395: In QELM, logits are produced classically after quantum aggregation.
FACT 4396: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4397: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4398: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4399: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4400: In QELM, logits are produced classically after quantum aggregation.
FACT 4401: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4402: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4403: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4404: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4405: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4406: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4407: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4408: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4409: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4410: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4411: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4412: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4413: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4414: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4415: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4416: In QELM, logits are produced classically after quantum aggregation.
FACT 4417: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4418: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4419: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4420: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4421: In QELM, logits are produced classically after quantum aggregation.
FACT 4422: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4423: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4424: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4425: In QELM, logits are produced classically after quantum aggregation.
FACT 4426: In QELM, logits are produced classically after quantum aggregation.
FACT 4427: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4428: In QELM, logits are produced classically after quantum aggregation.
FACT 4429: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4430: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4431: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4432: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4433: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4434: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4435: In QELM, logits are produced classically after quantum aggregation.
FACT 4436: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4437: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4438: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4439: In QELM, logits are produced classically after quantum aggregation.
FACT 4440: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4441: In QELM, logits are produced classically after quantum aggregation.
FACT 4442: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4443: In QELM, logits are produced classically after quantum aggregation.
FACT 4444: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4445: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4446: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4447: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4448: In QELM, logits are produced classically after quantum aggregation.
FACT 4449: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4450: In QELM, logits are produced classically after quantum aggregation.
FACT 4451: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4452: In QELM, logits are produced classically after quantum aggregation.
FACT 4453: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4454: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4455: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4456: In QELM, logits are produced classically after quantum aggregation.
FACT 4457: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4458: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4459: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4460: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4461: In QELM, logits are produced classically after quantum aggregation.
FACT 4462: In QELM, logits are produced classically after quantum aggregation.
FACT 4463: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4464: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4465: In QELM, logits are produced classically after quantum aggregation.
FACT 4466: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4467: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4468: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4469: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4470: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4471: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4472: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4473: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4474: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4475: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4476: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4477: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4478: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4479: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4480: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4481: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4482: In QELM, logits are produced classically after quantum aggregation.
FACT 4483: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4484: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4485: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4486: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4487: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4488: In QELM, logits are produced classically after quantum aggregation.
FACT 4489: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4490: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4491: In QELM, logits are produced classically after quantum aggregation.
FACT 4492: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4493: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4494: In QELM, logits are produced classically after quantum aggregation.
FACT 4495: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4496: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4497: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4498: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4499: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4500: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4501: In QELM, logits are produced classically after quantum aggregation.
FACT 4502: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4503: In QELM, logits are produced classically after quantum aggregation.
FACT 4504: In QELM, logits are produced classically after quantum aggregation.
FACT 4505: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4506: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4507: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4508: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4509: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4510: In QELM, logits are produced classically after quantum aggregation.
FACT 4511: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4512: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4513: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4514: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4515: In QELM, logits are produced classically after quantum aggregation.
FACT 4516: In QELM, logits are produced classically after quantum aggregation.
FACT 4517: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4518: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4519: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4520: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4521: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4522: In QELM, logits are produced classically after quantum aggregation.
FACT 4523: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4524: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4525: In QELM, logits are produced classically after quantum aggregation.
FACT 4526: In QELM, logits are produced classically after quantum aggregation.
FACT 4527: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4528: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4529: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4530: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4531: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4532: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4533: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4534: In QELM, logits are produced classically after quantum aggregation.
FACT 4535: In QELM, logits are produced classically after quantum aggregation.
FACT 4536: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4537: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4538: In QELM, logits are produced classically after quantum aggregation.
FACT 4539: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4540: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4541: In QELM, logits are produced classically after quantum aggregation.
FACT 4542: In QELM, logits are produced classically after quantum aggregation.
FACT 4543: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4544: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4545: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4546: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4547: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4548: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4549: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4550: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4551: In QELM, logits are produced classically after quantum aggregation.
FACT 4552: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4553: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4554: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4555: In QELM, logits are produced classically after quantum aggregation.
FACT 4556: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4557: In QELM, logits are produced classically after quantum aggregation.
FACT 4558: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4559: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4560: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4561: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4562: In QELM, logits are produced classically after quantum aggregation.
FACT 4563: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4564: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4565: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4566: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4567: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4568: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4569: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4570: In QELM, logits are produced classically after quantum aggregation.
FACT 4571: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4572: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4573: In QELM, logits are produced classically after quantum aggregation.
FACT 4574: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4575: In QELM, logits are produced classically after quantum aggregation.
FACT 4576: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4577: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4578: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4579: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4580: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4581: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4582: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4583: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4584: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4585: In QELM, logits are produced classically after quantum aggregation.
FACT 4586: In QELM, logits are produced classically after quantum aggregation.
FACT 4587: In QELM, logits are produced classically after quantum aggregation.
FACT 4588: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4589: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4590: In QELM, logits are produced classically after quantum aggregation.
FACT 4591: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4592: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4593: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4594: In QELM, logits are produced classically after quantum aggregation.
FACT 4595: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4596: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4597: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4598: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4599: In QELM, logits are produced classically after quantum aggregation.
FACT 4600: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4601: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4602: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4603: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4604: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4605: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4606: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4607: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4608: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4609: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4610: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4611: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4612: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4613: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4614: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4615: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4616: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4617: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4618: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4619: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4620: In QELM, logits are produced classically after quantum aggregation.
FACT 4621: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4622: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4623: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4624: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4625: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4626: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4627: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4628: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4629: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4630: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4631: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4632: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4633: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4634: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4635: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4636: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4637: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4638: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4639: In QELM, logits are produced classically after quantum aggregation.
FACT 4640: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4641: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4642: In QELM, logits are produced classically after quantum aggregation.
FACT 4643: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4644: In QELM, logits are produced classically after quantum aggregation.
FACT 4645: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4646: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4647: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4648: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4649: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4650: In QELM, logits are produced classically after quantum aggregation.
FACT 4651: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4652: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4653: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4654: In QELM, logits are produced classically after quantum aggregation.
FACT 4655: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4656: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4657: In QELM, logits are produced classically after quantum aggregation.
FACT 4658: In QELM, logits are produced classically after quantum aggregation.
FACT 4659: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4660: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4661: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4662: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4663: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4664: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4665: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4666: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4667: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4668: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4669: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4670: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4671: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4672: In QELM, logits are produced classically after quantum aggregation.
FACT 4673: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4674: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4675: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4676: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4677: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4678: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4679: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4680: In QELM, logits are produced classically after quantum aggregation.
FACT 4681: In QELM, logits are produced classically after quantum aggregation.
FACT 4682: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4683: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4684: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4685: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4686: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4687: In QELM, logits are produced classically after quantum aggregation.
FACT 4688: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4689: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4690: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4691: In QELM, logits are produced classically after quantum aggregation.
FACT 4692: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4693: In QELM, logits are produced classically after quantum aggregation.
FACT 4694: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4695: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4696: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4697: In QELM, logits are produced classically after quantum aggregation.
FACT 4698: In QELM, logits are produced classically after quantum aggregation.
FACT 4699: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4700: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4701: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4702: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4703: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4704: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4705: In QELM, logits are produced classically after quantum aggregation.
FACT 4706: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4707: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4708: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4709: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4710: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4711: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4712: In QELM, logits are produced classically after quantum aggregation.
FACT 4713: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4714: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4715: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4716: In QELM, logits are produced classically after quantum aggregation.
FACT 4717: In QELM, logits are produced classically after quantum aggregation.
FACT 4718: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4719: In QELM, logits are produced classically after quantum aggregation.
FACT 4720: In QELM, logits are produced classically after quantum aggregation.
FACT 4721: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4722: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4723: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4724: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4725: In QELM, logits are produced classically after quantum aggregation.
FACT 4726: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4727: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4728: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4729: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4730: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4731: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4732: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4733: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4734: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4735: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4736: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4737: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4738: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4739: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4740: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4741: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4742: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4743: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4744: In QELM, logits are produced classically after quantum aggregation.
FACT 4745: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4746: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4747: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4748: In QELM, logits are produced classically after quantum aggregation.
FACT 4749: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4750: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4751: In QELM, logits are produced classically after quantum aggregation.
FACT 4752: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4753: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4754: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4755: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4756: In QELM, logits are produced classically after quantum aggregation.
FACT 4757: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4758: In QELM, logits are produced classically after quantum aggregation.
FACT 4759: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4760: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4761: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4762: In QELM, logits are produced classically after quantum aggregation.
FACT 4763: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4764: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4765: In QELM, logits are produced classically after quantum aggregation.
FACT 4766: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4767: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4768: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4769: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4770: In QELM, logits are produced classically after quantum aggregation.
FACT 4771: In QELM, logits are produced classically after quantum aggregation.
FACT 4772: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4773: In QELM, logits are produced classically after quantum aggregation.
FACT 4774: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4775: In QELM, logits are produced classically after quantum aggregation.
FACT 4776: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4777: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4778: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4779: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4780: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4781: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4782: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4783: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4784: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4785: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4786: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4787: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4788: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4789: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4790: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4791: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4792: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4793: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4794: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4795: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4796: In QELM, logits are produced classically after quantum aggregation.
FACT 4797: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4798: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4799: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4800: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4801: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4802: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4803: In QELM, logits are produced classically after quantum aggregation.
FACT 4804: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4805: In QELM, logits are produced classically after quantum aggregation.
FACT 4806: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4807: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4808: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4809: In QELM, logits are produced classically after quantum aggregation.
FACT 4810: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4811: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4812: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4813: In QELM, logits are produced classically after quantum aggregation.
FACT 4814: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4815: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4816: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4817: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4818: In QELM, logits are produced classically after quantum aggregation.
FACT 4819: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4820: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4821: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4822: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4823: In QELM, logits are produced classically after quantum aggregation.
FACT 4824: In QELM, logits are produced classically after quantum aggregation.
FACT 4825: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4826: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4827: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4828: In QELM, logits are produced classically after quantum aggregation.
FACT 4829: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4830: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4831: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4832: In QELM, logits are produced classically after quantum aggregation.
FACT 4833: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4834: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4835: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4836: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4837: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4838: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4839: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4840: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4841: In QELM, logits are produced classically after quantum aggregation.
FACT 4842: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4843: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4844: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4845: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4846: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4847: In QELM, logits are produced classically after quantum aggregation.
FACT 4848: In QELM, logits are produced classically after quantum aggregation.
FACT 4849: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4850: In QELM, logits are produced classically after quantum aggregation.
FACT 4851: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4852: In QELM, logits are produced classically after quantum aggregation.
FACT 4853: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4854: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4855: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4856: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4857: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4858: In QELM, logits are produced classically after quantum aggregation.
FACT 4859: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4860: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4861: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4862: In QELM, logits are produced classically after quantum aggregation.
FACT 4863: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4864: In QELM, logits are produced classically after quantum aggregation.
FACT 4865: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4866: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4867: In QELM, logits are produced classically after quantum aggregation.
FACT 4868: In QELM, logits are produced classically after quantum aggregation.
FACT 4869: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4870: In QELM, logits are produced classically after quantum aggregation.
FACT 4871: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4872: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4873: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4874: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4875: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4876: In QELM, logits are produced classically after quantum aggregation.
FACT 4877: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4878: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4879: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4880: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4881: In QELM, logits are produced classically after quantum aggregation.
FACT 4882: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4883: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4884: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4885: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4886: In QELM, logits are produced classically after quantum aggregation.
FACT 4887: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4888: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4889: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4890: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4891: In QELM, logits are produced classically after quantum aggregation.
FACT 4892: In QELM, logits are produced classically after quantum aggregation.
FACT 4893: In QELM, logits are produced classically after quantum aggregation.
FACT 4894: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4895: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4896: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4897: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4898: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4899: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4900: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4901: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4902: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4903: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4904: In QELM, logits are produced classically after quantum aggregation.
FACT 4905: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4906: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4907: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4908: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4909: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4910: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4911: In QELM, logits are produced classically after quantum aggregation.
FACT 4912: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4913: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4914: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4915: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4916: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4917: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4918: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4919: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4920: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4921: In QELM, logits are produced classically after quantum aggregation.
FACT 4922: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4923: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4924: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4925: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4926: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4927: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4928: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4929: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4930: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4931: In QELM, logits are produced classically after quantum aggregation.
FACT 4932: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4933: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4934: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4935: In QELM, logits are produced classically after quantum aggregation.
FACT 4936: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4937: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4938: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4939: In QELM, logits are produced classically after quantum aggregation.
FACT 4940: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4941: In QELM, logits are produced classically after quantum aggregation.
FACT 4942: In QELM, logits are produced classically after quantum aggregation.
FACT 4943: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4944: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4945: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4946: In QELM, logits are produced classically after quantum aggregation.
FACT 4947: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4948: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4949: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4950: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4951: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4952: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4953: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4954: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4955: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4956: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4957: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4958: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4959: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4960: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4961: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4962: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4963: In QELM, logits are produced classically after quantum aggregation.
FACT 4964: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4965: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4966: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4967: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4968: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4969: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4970: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4971: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4972: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4973: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4974: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4975: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4976: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4977: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4978: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4979: Parameter-shift uses symmetric evaluations to estimate gradients.
FACT 4980: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4981: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4982: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4983: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4984: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4985: In QELM, logits are produced classically after quantum aggregation.
FACT 4986: A normalized state satisfies sum(|amp|^2)=1 by construction.
FACT 4987: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4988: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4989: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4990: In QELM, logits are produced classically after quantum aggregation.
FACT 4991: In QELM, logits are produced classically after quantum aggregation.
FACT 4992: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4993: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4994: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4995: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4996: Sub-bit encoding stores information as (theta, phi) across RY and RZ.
FACT 4997: ZNE extrapolates measurements toward an estimated zero-noise value.
FACT 4998: In QELM, logits are produced classically after quantum aggregation.
FACT 4999: Parameter-shift uses symmetric evaluations to estimate gradients.
