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<p align="center"> English | <a href="README_cn.md"> 简体中文 </a></p>

TensorCircuit-NG is the next-generation open-source high-performance quantum software framework, and the world's first [AI-native quantum programming platform](https://tensorcircuit-ng.readthedocs.io/en/latest/agent_landing/index.html) purpose-built for agentic research and automated scientific discovery.

TensorCircuit-NG is built upon tensornetwork engines, supporting for automatic differentiation, just-in-time compiling, hardware acceleration, vectorized parallelism and distributed training, providing unified infrastructures and interfaces for quantum programming. It can compose quantum circuits, neural networks and tensor networks seamlessly with high simulation efficiency and flexibility.

TensorCircuit-NG is built on top of modern machine learning frameworks: Jax, TensorFlow, and PyTorch. It is specifically suitable for large-scale simulations of quantum-classical hybrid paradigm and variational quantum algorithms in ideal (`Circuit`), noisy (`DMCircuit`), Clifford (`StabilizerCircuit`), qudit (`QuditCircuit`), approximate (`MPSCircuit`), analog (`AnalogCircuit`), symmetric (`U1Circuit`) and fermionic (`FGSCircuit`) cases. It also supports quantum hardware access and provides CPU/GPU/QPU hybrid deployment solutions.

TensorCircuit-NG is the technical successor to TensorCircuit, led and maintained by the original TensorCircuit development team. This distribution has served as the primary home for the framework's evolution, addressing critical maintenance gaps (numpy > 2.0, qiskit > 1.0) and feature enhancements. As a fully compatible [drop-in replacement](https://tensorcircuit-ng.readthedocs.io/en/latest/faq.html#what-is-the-relation-between-tensorcircuit-and-tensorcircuit-ng), TensorCircuit-NG delivers next-gen capabilities—including stabilizer/qudit/analog/symmetric circuit simulation and multi-node multi-GPU distributed simulation.


## Getting Started

Please begin with [Quick Start](/docs/source/quickstart.rst) in the [full documentation](https://tensorcircuit-ng.readthedocs.io/).

For more information on software usage, sota algorithm implementation and engineer paradigm demonstration, please refer to 170+ [example scripts](/examples) and 40+ [tutorial notebooks](https://tensorcircuit-ng.readthedocs.io/en/latest/#tutorials). API docstrings and test cases in [tests](/tests) are also informative. One can also refer to AI-native docs for tensorcircuit-ng: [Devin Deepwiki](https://deepwiki.com/tensorcircuit/tensorcircuit-ng), [Google Code Wiki](https://codewiki.google/github.com/tensorcircuit/tensorcircuit-ng), and [Context7 MCP](https://context7.com/tensorcircuit/tensorcircuit-ng).

For beginners, please refer to [quantum computing lectures with TC-NG](https://github.com/sxzgroup/qc_lecture) to learn both quantum computing basics and representative usage of TensorCircuit-NG.

### AI-Native R&D (Recommended)

To write TC-NG scripts and applications efficiently with AI coding agents (e.g., Claude Code, Cursor, Antigravity), we strongly recommend **working directly within the local tensorcircuit-ng repository** rather than an empty folder.

1.  **Rich Context:** The 100+ scripts in `examples/` and extensive test cases in `tests/` provide essential references that significantly reduce AI hallucinations.
2.  **Built-in Rules:** We provide a dedicated [AGENTS.md](/AGENTS.md) file. It serves as the "handbook" (i.e. `CLAUDE.md`) for AI agents, defining coding standards and best practices to ensure the generated code is idiomatic.
3.  **Specialized Agentic Skills:** The `.agents/skills/` directory contains workflows to guide AI assistants on complex, multi-step tasks.
<details>
<summary> List of built-in agentic skills (click for details) </summary>

  *   [`arxiv-reproduce`](/.agents/skills/arxiv-reproduce/README.md): Autonomously reproduces arXiv papers with standardized output and code quality validation.
  *   [`performance-optimize`](/.agents/skills/performance-optimize/README.md): Scientific execution and memory optimization workflow (JAX scanning, vectorized parallelism, etc.).
  *   [`tc-rosetta`](/.agents/skills/tc-rosetta/README.md): End-to-end framework translation (from Qiskit, PennyLane, etc.) with intrinsic mathematical intent rewriting.
  *   [`tutorial-crafter`](/.agents/skills/tutorial-crafter/README.md): Transforms raw TC-NG scripts into comprehensive, narrative-driven Markdown or/and HTML educational tutorials.
  *   [`demo-generator`](/.agents/skills/demo-generator/README.md): Transforms TC-NG scripts into interactive, sleek, and high-performance Streamlit GUI applications.
  *   [`code-reviewer`](/.agents/skills/code-reviewer/README.md): Autonomously reviews and refactors TC-NG code for mathematical correctness, JAX-native performance, and engineering rigor.
  *   [`sanity-checker`](/.agents/skills/sanity-checker/README.md): Systematic audit and refactoring to reduce technical debt, improve abstractions, and ensure codebase health.
  *   [`meta-explorer`](/.agents/skills/meta-explorer/README.md): High-intensity autonomous research agent for circuit architecture and optimization strategy discovery (VQE, QML, QAOA, etc.).

</details>


**Recommended Workflow:**

1.  Clone the repository: `git clone https://github.com/tensorcircuit/tensorcircuit-ng.git`
2.  Switch to a local playground branch: `git checkout -b my-playground` in case messing up with the original repository.
3.  Open the repository folder in your AI IDE. And you are ready to start writing TC-NG-based scripts.

Now, enjoy implementing quantum algorithms entirely through natural language! By seamlessly integrating the extreme performance with an autonomous, intent-driven AI workflow (via embedded `.agents/skills/`), TC-NG empowers researchers to transition from manual coding to automated paper reproduction, intelligent performance squeezing, and cross-framework translation in seconds.

### Quick Demos

The following are some minimal demos.

- Circuit construction:

```python
import tensorcircuit as tc
c = tc.Circuit(2)
c.H(0)
c.CNOT(0,1)
c.rx(1, theta=0.2)
print(c.wavefunction())
print(c.expectation_ps(z=[0, 1]))
print(c.sample(allow_state=True, batch=1024, format="count_dict_bin"))
```

- Runtime behavior customization:

```python
tc.set_backend("jax")
tc.set_dtype("complex128")
tc.set_contractor("cotengra")
```

- Automatic differentiation with jit:

```python
def forward(theta):
    c = tc.Circuit(2)
    c.R(0, theta=theta, alpha=0.5, phi=0.8)
    return tc.backend.real(c.expectation((tc.gates.z(), [0])))

g = tc.backend.grad(forward)
g = tc.backend.jit(g)
theta = tc.array_to_tensor(1.0)
print(g(theta))
```

<details>
  <summary> More highlight features for TensorCircuit (click for details) </summary>

- Sparse Hamiltonian generation and expectation evaluation:

```python
n = 6
pauli_structures = []
weights = []
for i in range(n):
    pauli_structures.append(tc.quantum.xyz2ps({"z": [i, (i + 1) % n]}, n=n))
    weights.append(1.0)
for i in range(n):
    pauli_structures.append(tc.quantum.xyz2ps({"x": [i]}, n=n))
    weights.append(-1.0)
h = tc.quantum.PauliStringSum2COO(pauli_structures, weights)
print(h)
# BCOO(complex64[64, 64], nse=448)
c = tc.Circuit(n)
c.h(range(n))
energy = tc.templates.measurements.operator_expectation(c, h)
# -6
```

- Large-scale simulation with tensor network engine

```python
# tc.set_contractor("cotengra-30-10")
n=500
c = tc.Circuit(n)
c.h(0)
c.cx(range(n-1), range(1, n))
c.expectation_ps(z=[0, n-1], reuse=False)
```

- Density matrix simulator and quantum info quantities

```python
c = tc.DMCircuit(2)
c.h(0)
c.cx(0, 1)
c.depolarizing(1, px=0.1, py=0.1, pz=0.1)
dm = c.state()
print(tc.quantum.entropy(dm))
print(tc.quantum.entanglement_entropy(dm, [0]))
print(tc.quantum.entanglement_negativity(dm, [0]))
print(tc.quantum.log_negativity(dm, [0]))
```

</details>

## Install

The package is written in pure Python and can be obtained via pip as:

```python
pip install tensorcircuit-ng
```

We recommend you install this package with tensorflow or jax also installed as:

```python
pip install "tensorcircuit-ng[tensorflow]"
```

Other optional dependencies include `[torch]`, `[jax]`, `[qiskit]` and `[cloud]`.

Try nightly build for the newest features:

```python
pip install tensorcircuit-nightly
```

## Advantages

- Tensor network simulation engine based

- JIT, AD, vectorized parallelism compatible

- GPU support, QPU access support, hybrid deployment support

- HPC native, distributed simulation enabled, multiple devices/hosts support

- Efficiency
  - Time: 10 to 10^6+ times acceleration compared to TensorFlow Quantum, Pennylane, CuQuantum, TorchQuantum or Qiskit

  - Space: 600+ qubits 1D VQE workflow (converged energy inaccuracy: < 1%)

- Elegance
  - Flexibility: customized contraction, multiple ML backend/interface choices, multiple dtype precisions, multiple QPU providers

  - API design: quantum for humans, less code, more power

- Batteries included

  <details>
  <summary> Tons of amazing features and built in tools for research (click for details) </summary>

  - Support **super large circuit simulation** using tensor network engine.

  - Support **noisy simulation** with both Monte Carlo and density matrix (tensor network powered) modes.

  - Support **stabilizer circuit simulation** with stim backend.

  - Support **approximate simulation** with MPS-TEBD modes.

  - Support **analog/digital hybrid simulation** (time dependent Hamiltonian evolution, **pulse** level simulation) with neural ode modes.

  - Support **Fermion Gaussian state** simulation with expectation, entanglement, measurement, ground state, real and imaginary time evolution.

  - Support **qudits simulation** for tensor network and MPS approximation modes.

  - Support **parallel** quantum circuit evaluation across **multiple GPUs** and **multiple hosts**.

  - Highly customizable **noise model** with gate error and scalable readout error.

  - Support for **non-unitary** gate and post-selection simulation.

  - Support **real quantum devices access** from different providers.

  - **Scalable readout error mitigation** native to both bitstring and expectation level with automatic qubit mapping consideration.

  - **Advanced quantum error mitigation methods** and pipelines such as ZNE, DD, RC, etc.

  - Support **MPS/MPO** as representations for input states, quantum gates and observables to be measured.

  - Support **vectorized parallelism** on circuit inputs, circuit parameters, circuit structures, circuit measurements and these vectorization can be nested.

  - Gradients can be obtained with both **automatic differenation** and parameter shift (vmap accelerated) modes.

  - **Machine learning interface/layer/model** abstraction in both TensorFlow, PyTorch and Jax for both numerical simulation and real QPU experiments.

  - Support time evolution simulation with **exact, ODE, Krylov, Trotter, Chebyshev solvers**.

  - Support **symmetry-enforced circuit simulation** with `U1Circuit` for charge conservation.

  - Support Heisenberg picture-based **Pauli propagation** approximation simulation for circuits.

  - Circuit sampling supports both final state sampling and perfect sampling from tensor networks.

  - Light cone reduction support for local expectation calculation.

  - Highly customizable tensor network contraction path finder with opteinsum and cotengra interface.

  - Observables are supported in measurement, sparse matrix, dense matrix and MPO format.

  - Super fast weighted sum Pauli string Hamiltonian matrix generation.

  - Reusable common circuit/measurement/problem templates and patterns.

  - Jittable classical shadow infrastructures.

  - SOTA quantum algorithm and model implementations.

  - Support hybrid workflows and pipelines with CPU/GPU/QPU hardware from local/cloud/hpc resources using tf/torch/jax/cupy/numpy frameworks all at the same time.

  - Support **autonomous paper reproduction**.

  - Support **autonomous research discovery** for circuit architectures and optimization strategies.

  - Fully **AI-native ecosystem** with built-in agentic skills and standardized development rules for AI assistants.

  </details>

## Contributing

### Status

This project is created and maintained by [Shi-Xin Zhang](https://github.com/refraction-ray) with current core authors [Shi-Xin Zhang](https://github.com/refraction-ray) and [Yu-Qin Chen](https://github.com/yutuer21) (see the [brief history](/HISTORY.md) of TensorCircuit and TensorCircuit-NG). We also thank [contributions](https://github.com/tensorcircuit/tensorcircuit-ng/graphs/contributors) from the open source community.

### Citation

If this project helps in your research, please cite the two versions of software whitepapers to acknowledge the work put into the development of TensorCircuit-NG.

- [TensorCircuit: a Quantum Software Framework for the NISQ Era](https://quantum-journal.org/papers/q-2023-02-02-912/) (published in Quantum).

- [TensorCircuit-NG: A Universal, Composable, and Scalable Platform for Quantum Computing and Quantum Simulation](https://arxiv.org/abs/2602.14167).

These two works also serve as a good introduction to the software.

Research works citing TensorCircuit-NG can be highlighted in [Research and Applications section](https://github.com/tensorcircuit/tensorcircuit-ng#research-and-applications).

### Guidelines

For contribution guidelines and notes, see [CONTRIBUTING](/CONTRIBUTING.md).

We welcome [issues](https://github.com/tensorcircuit/tensorcircuit-ng/issues), [PRs](https://github.com/tensorcircuit/tensorcircuit-ng/pulls), and [discussions](https://github.com/tensorcircuit/tensorcircuit-ng/discussions) from everyone, and these are all hosted on GitHub.

### License

TensorCircuit-NG is open source, released under the Apache License, Version 2.0.

### Contributors

<!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->
<!-- prettier-ignore-start -->
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<table>
  <tbody>
    <tr>
      <td align="center" valign="top" width="16.66%"><a href="https://re-ra.xyz"><img src="https://avatars.githubusercontent.com/u/35157286?v=4?s=100" width="100px;" alt="Shixin Zhang"/><br /><sub><b>Shixin Zhang</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=refraction-ray" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=refraction-ray" title="Documentation">📖</a> <a href="#example-refraction-ray" title="Examples">💡</a> <a href="#ideas-refraction-ray" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-refraction-ray" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="#maintenance-refraction-ray" title="Maintenance">🚧</a> <a href="#research-refraction-ray" title="Research">🔬</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/pulls?q=is%3Apr+reviewed-by%3Arefraction-ray" title="Reviewed Pull Requests">👀</a> <a href="#translation-refraction-ray" title="Translation">🌍</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=refraction-ray" title="Tests">⚠️</a> <a href="#tutorial-refraction-ray" title="Tutorials">✅</a> <a href="#talk-refraction-ray" title="Talks">📢</a> <a href="#question-refraction-ray" title="Answering Questions">💬</a> <a href="#financial-refraction-ray" title="Financial">💵</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/yutuer21"><img src="https://avatars.githubusercontent.com/u/83822724?v=4?s=100" width="100px;" alt="Yuqin Chen"/><br /><sub><b>Yuqin Chen</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=yutuer21" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=yutuer21" title="Documentation">📖</a> <a href="#example-yutuer21" title="Examples">💡</a> <a href="#ideas-yutuer21" title="Ideas, Planning, & Feedback">🤔</a> <a href="#research-yutuer21" title="Research">🔬</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=yutuer21" title="Tests">⚠️</a> <a href="#tutorial-yutuer21" title="Tutorials">✅</a> <a href="#talk-yutuer21" title="Talks">📢</a></td>
      <td align="center" valign="top" width="16.66%"><a href="http://jiezhongqiu.com"><img src="https://avatars.githubusercontent.com/u/3853009?v=4?s=100" width="100px;" alt="Jiezhong Qiu"/><br /><sub><b>Jiezhong Qiu</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=xptree" title="Code">💻</a> <a href="#example-xptree" title="Examples">💡</a> <a href="#ideas-xptree" title="Ideas, Planning, & Feedback">🤔</a> <a href="#research-xptree" title="Research">🔬</a></td>
      <td align="center" valign="top" width="16.66%"><a href="http://liwt31.github.io"><img src="https://avatars.githubusercontent.com/u/22628546?v=4?s=100" width="100px;" alt="Weitang Li"/><br /><sub><b>Weitang Li</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=liwt31" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=liwt31" title="Documentation">📖</a> <a href="#ideas-liwt31" title="Ideas, Planning, & Feedback">🤔</a> <a href="#research-liwt31" title="Research">🔬</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=liwt31" title="Tests">⚠️</a> <a href="#talk-liwt31" title="Talks">📢</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/SUSYUSTC"><img src="https://avatars.githubusercontent.com/u/30529122?v=4?s=100" width="100px;" alt="Jiace Sun"/><br /><sub><b>Jiace Sun</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=SUSYUSTC" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=SUSYUSTC" title="Documentation">📖</a> <a href="#example-SUSYUSTC" title="Examples">💡</a> <a href="#ideas-SUSYUSTC" title="Ideas, Planning, & Feedback">🤔</a> <a href="#research-SUSYUSTC" title="Research">🔬</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=SUSYUSTC" title="Tests">⚠️</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/Zhouquan-Wan"><img src="https://avatars.githubusercontent.com/u/54523490?v=4?s=100" width="100px;" alt="Zhouquan Wan"/><br /><sub><b>Zhouquan Wan</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Zhouquan-Wan" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Zhouquan-Wan" title="Documentation">📖</a> <a href="#example-Zhouquan-Wan" title="Examples">💡</a> <a href="#ideas-Zhouquan-Wan" title="Ideas, Planning, & Feedback">🤔</a> <a href="#research-Zhouquan-Wan" title="Research">🔬</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Zhouquan-Wan" title="Tests">⚠️</a> <a href="#tutorial-Zhouquan-Wan" title="Tutorials">✅</a></td>
    </tr>
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      <td align="center" valign="top" width="16.66%"><a href="https://github.com/ls-iastu"><img src="https://avatars.githubusercontent.com/u/70554346?v=4?s=100" width="100px;" alt="Shuo Liu"/><br /><sub><b>Shuo Liu</b></sub></a><br /><a href="#example-ls-iastu" title="Examples">💡</a> <a href="#research-ls-iastu" title="Research">🔬</a> <a href="#tutorial-ls-iastu" title="Tutorials">✅</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/YHPeter"><img src="https://avatars.githubusercontent.com/u/44126839?v=4?s=100" width="100px;" alt="Hao Yu"/><br /><sub><b>Hao Yu</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=YHPeter" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=YHPeter" title="Documentation">📖</a> <a href="#infra-YHPeter" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=YHPeter" title="Tests">⚠️</a> <a href="#tutorial-YHPeter" title="Tutorials">✅</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/SexyCarrots"><img src="https://avatars.githubusercontent.com/u/63588721?v=4?s=100" width="100px;" alt="Xinghan Yang"/><br /><sub><b>Xinghan Yang</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=SexyCarrots" title="Documentation">📖</a> <a href="#translation-SexyCarrots" title="Translation">🌍</a> <a href="#tutorial-SexyCarrots" title="Tutorials">✅</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/JachyMeow"><img src="https://avatars.githubusercontent.com/u/114171061?v=4?s=100" width="100px;" alt="JachyMeow"/><br /><sub><b>JachyMeow</b></sub></a><br /><a href="#tutorial-JachyMeow" title="Tutorials">✅</a> <a href="#translation-JachyMeow" title="Translation">🌍</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/Mzye21"><img src="https://avatars.githubusercontent.com/u/86239031?v=4?s=100" width="100px;" alt="Zhaofeng Ye"/><br /><sub><b>Zhaofeng Ye</b></sub></a><br /><a href="#design-Mzye21" title="Design">🎨</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/erertertet"><img src="https://avatars.githubusercontent.com/u/41342153?v=4?s=100" width="100px;" alt="erertertet"/><br /><sub><b>erertertet</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=erertertet" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=erertertet" title="Documentation">📖</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=erertertet" title="Tests">⚠️</a></td>
    </tr>
    <tr>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/yicongzheng"><img src="https://avatars.githubusercontent.com/u/107173985?v=4?s=100" width="100px;" alt="Yicong Zheng"/><br /><sub><b>Yicong Zheng</b></sub></a><br /><a href="#tutorial-yicongzheng" title="Tutorials">✅</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://marksong.tech"><img src="https://avatars.githubusercontent.com/u/78847784?v=4?s=100" width="100px;" alt="Zixuan Song"/><br /><sub><b>Zixuan Song</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=MarkSong535" title="Documentation">📖</a> <a href="#translation-MarkSong535" title="Translation">🌍</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=MarkSong535" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=MarkSong535" title="Tests">⚠️</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/buwantaiji"><img src="https://avatars.githubusercontent.com/u/25216189?v=4?s=100" width="100px;" alt="Hao Xie"/><br /><sub><b>Hao Xie</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=buwantaiji" title="Documentation">📖</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/pramitsingh0"><img src="https://avatars.githubusercontent.com/u/52959209?v=4?s=100" width="100px;" alt="Pramit Singh"/><br /><sub><b>Pramit Singh</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=pramitsingh0" title="Tests">⚠️</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/JAllcock"><img src="https://avatars.githubusercontent.com/u/26302022?v=4?s=100" width="100px;" alt="Jonathan Allcock"/><br /><sub><b>Jonathan Allcock</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=JAllcock" title="Documentation">📖</a> <a href="#ideas-JAllcock" title="Ideas, Planning, & Feedback">🤔</a> <a href="#talk-JAllcock" title="Talks">📢</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/nealchen2003"><img src="https://avatars.githubusercontent.com/u/45502551?v=4?s=100" width="100px;" alt="nealchen2003"/><br /><sub><b>nealchen2003</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=nealchen2003" title="Documentation">📖</a></td>
    </tr>
    <tr>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/eurethia"><img src="https://avatars.githubusercontent.com/u/84611606?v=4?s=100" width="100px;" alt="隐公观鱼"/><br /><sub><b>隐公观鱼</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=eurethia" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=eurethia" title="Tests">⚠️</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/WiuYuan"><img src="https://avatars.githubusercontent.com/u/108848998?v=4?s=100" width="100px;" alt="WiuYuan"/><br /><sub><b>WiuYuan</b></sub></a><br /><a href="#example-WiuYuan" title="Examples">💡</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://www.linkedin.com/in/felix-xu-16a153196/"><img src="https://avatars.githubusercontent.com/u/61252303?v=4?s=100" width="100px;" alt="Felix Xu"/><br /><sub><b>Felix Xu</b></sub></a><br /><a href="#tutorial-FelixXu35" title="Tutorials">✅</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=FelixXu35" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=FelixXu35" title="Tests">⚠️</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://scholar.harvard.edu/hongyehu/home"><img src="https://avatars.githubusercontent.com/u/50563225?v=4?s=100" width="100px;" alt="Hong-Ye Hu"/><br /><sub><b>Hong-Ye Hu</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=hongyehu" title="Documentation">📖</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/PeilinZHENG"><img src="https://avatars.githubusercontent.com/u/45784888?v=4?s=100" width="100px;" alt="peilin"/><br /><sub><b>peilin</b></sub></a><br /><a href="#tutorial-PeilinZHENG" title="Tutorials">✅</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=PeilinZHENG" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=PeilinZHENG" title="Tests">⚠️</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=PeilinZHENG" title="Documentation">📖</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://emilianog-byte.github.io"><img src="https://avatars.githubusercontent.com/u/57567043?v=4?s=100" width="100px;" alt="Cristian Emiliano Godinez Ramirez"/><br /><sub><b>Cristian Emiliano Godinez Ramirez</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=EmilianoG-byte" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=EmilianoG-byte" title="Tests">⚠️</a></td>
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    <tr>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/ztzhu1"><img src="https://avatars.githubusercontent.com/u/111620128?v=4?s=100" width="100px;" alt="ztzhu"/><br /><sub><b>ztzhu</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=ztzhu1" title="Code">💻</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/royess"><img src="https://avatars.githubusercontent.com/u/31059422?v=4?s=100" width="100px;" alt="Rabqubit"/><br /><sub><b>Rabqubit</b></sub></a><br /><a href="#example-royess" title="Examples">💡</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/king-p3nguin"><img src="https://avatars.githubusercontent.com/u/103920010?v=4?s=100" width="100px;" alt="Kazuki Tsuoka"/><br /><sub><b>Kazuki Tsuoka</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=king-p3nguin" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=king-p3nguin" title="Tests">⚠️</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=king-p3nguin" title="Documentation">📖</a> <a href="#example-king-p3nguin" title="Examples">💡</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://gopal-dahale.github.io/"><img src="https://avatars.githubusercontent.com/u/49199003?v=4?s=100" width="100px;" alt="Gopal Ramesh Dahale"/><br /><sub><b>Gopal Ramesh Dahale</b></sub></a><br /><a href="#example-Gopal-Dahale" title="Examples">💡</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/AbdullahKazi500"><img src="https://avatars.githubusercontent.com/u/75779966?v=4?s=100" width="100px;" alt="Chanandellar Bong"/><br /><sub><b>Chanandellar Bong</b></sub></a><br /><a href="#example-AbdullahKazi500" title="Examples">💡</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://adeshpande.gitlab.io"><img src="https://avatars.githubusercontent.com/u/6169877?v=4?s=100" width="100px;" alt="Abhinav Deshpande"/><br /><sub><b>Abhinav Deshpande</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=abhinavd" title="Code">💻</a></td>
    </tr>
    <tr>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/Stellogic"><img src="https://avatars.githubusercontent.com/u/186928579?v=4?s=100" width="100px;" alt="Stellogic"/><br /><sub><b>Stellogic</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Stellogic" title="Code">💻</a> <a href="#example-Stellogic" title="Examples">💡</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Stellogic" title="Tests">⚠️</a> <a href="#tutorial-Stellogic" title="Tutorials">✅</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/Charlespkuer"><img src="https://avatars.githubusercontent.com/u/112697147?v=4?s=100" width="100px;" alt="Huang"/><br /><sub><b>Huang</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Charlespkuer" title="Code">💻</a> <a href="#example-Charlespkuer" title="Examples">💡</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Charlespkuer" title="Tests">⚠️</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/Huang-Xu-Yang"><img src="https://avatars.githubusercontent.com/u/227286661?v=4?s=100" width="100px;" alt="Huang-Xu-Yang"/><br /><sub><b>Huang-Xu-Yang</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Huang-Xu-Yang" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Huang-Xu-Yang" title="Tests">⚠️</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/WeiguoMa"><img src="https://avatars.githubusercontent.com/u/108172530?v=4?s=100" width="100px;" alt="Weiguo_M"/><br /><sub><b>Weiguo_M</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=WeiguoMa" title="Code">💻</a> <a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=WeiguoMa" title="Tests">⚠️</a> <a href="#example-WeiguoMa" title="Examples">💡</a> <a href="#tutorial-WeiguoMa" title="Tutorials">✅</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/QuiXamii"><img src="https://avatars.githubusercontent.com/u/136054857?v=4?s=100" width="100px;" alt="Qixiang WANG"/><br /><sub><b>Qixiang WANG</b></sub></a><br /><a href="#example-QuiXamii" title="Examples">💡</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/iop-hui252"><img src="https://avatars.githubusercontent.com/u/257909307?v=4?s=100" width="100px;" alt="iop-hui252"/><br /><sub><b>iop-hui252</b></sub></a><br /><a href="#example-iop-hui252" title="Examples">💡</a></td>
    </tr>
    <tr>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/Yoshiyuki-F"><img src="https://avatars.githubusercontent.com/u/45096493?v=4?s=100" width="100px;" alt="Yoshiyuki-F"/><br /><sub><b>Yoshiyuki-F</b></sub></a><br /><a href="https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Yoshiyuki-F" title="Code">💻</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/QingyunQian"><img src="https://avatars.githubusercontent.com/u/69110244?v=4?s=100" width="100px;" alt="QingyunQian"/><br /><sub><b>QingyunQian</b></sub></a><br /><a href="#example-QingyunQian" title="Examples">💡</a></td>
      <td align="center" valign="top" width="16.66%"><a href="https://github.com/DeanTMaxim"><img src="https://avatars.githubusercontent.com/u/22721535?v=4?s=100" width="100px;" alt="DeanT.Maxim"/><br /><sub><b>DeanT.Maxim</b></sub></a><br /><a href="#example-DeanTMaxim" title="Examples">💡</a></td>
    </tr>
  </tbody>
</table>

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## Research and Applications

TensorCircuit-NG is a powerful framework for driving research and applications in quantum computing. Below are examples of published academic works (150+ in total) and open-source projects that utilize TensorCircuit and TensorCircuit-NG.

### DQAS

For the application of Differentiable Quantum Architecture Search, see [applications](/tensorcircuit/applications).

Reference paper: https://arxiv.org/abs/2010.08561 (published in QST).

### VQNHE

For the application of Variational Quantum-Neural Hybrid Eigensolver, see [applications](/tensorcircuit/applications).

Reference paper: https://arxiv.org/abs/2106.05105 (published in PRL) and https://arxiv.org/abs/2112.10380 (published in AQT).

### VQEX-MBL

For the application of VQEX on MBL phase identification, see the [tutorial](/docs/source/tutorials/vqex_mbl.ipynb).

Reference paper: https://arxiv.org/abs/2111.13719 (published in PRB).

### Stark-DTC

For the numerical demosntration of discrete time crystal enabled by Stark many-body localization, see the Floquet simulation [demo](/examples/timeevolution_trotter.py).

Reference paper: https://arxiv.org/abs/2208.02866 (published in PRL).

### RA-Training

For the numerical simulation of variational quantum algorithm training using random gate activation strategy by us, see the [project repo](https://github.com/ls-iastu/RAtraining).

Reference paper: https://arxiv.org/abs/2303.08154 (published in PRR as a Letter).

### TenCirChem

[TenCirChem](https://github.com/tencent-quantum-lab/TenCirChem) is an efficient and versatile quantum computation package for molecular properties. TenCirChem is based on TensorCircuit and is optimized for chemistry applications. The latest version TenCirChem-NG is open source and available at [TenCirChem-NG](https://github.com/tensorcircuit/TenCirChem-NG).

Reference paper: https://arxiv.org/abs/2303.10825 (published in JCTC).

### EMQAOA-DARBO

For the numerical simulation and hardware experiments with error mitigation on QAOA, see the [project repo](https://github.com/sherrylixuecheng/EMQAOA-DARBO).

Reference paper: https://arxiv.org/abs/2303.14877 (published in Communications Physics).

### NN-VQA

For the setup and simulation code of neural network encoded variational quantum eigensolver, see the [demo](/docs/source/tutorials/nnvqe.ipynb).

Reference paper: https://arxiv.org/abs/2308.01068 (published in PRApplied).

### FLDC

Absence of barren plateaus in finite local-depth circuits with long-range entanglement, see the [demo](/examples/vqe_toric_code.py).

Reference paper: https://arxiv.org/abs/2311.01393 (published in PRL).

### Effective temperature in ansatzes

For the simulation implementation of quantum states based on neural networks, tensor networs and quantum circuits using TensorCircuit-NG, see the [project repo](https://github.com/sxzgroup/et).

Reference paper: https://arxiv.org/abs/2411.18921 (published in PRR).

### A Unified Variational Framework for Quantum Excited States

For the simulation code and data for variational optimization of simutaneous excited states, see the [project repo](https://github.com/sxzgroup/quantum_excited_state).

Reference paper: https://arxiv.org/abs/2504.21459.

### Quantum Machine Unlearning

For the simulation code for the work "superior resilience to poisoning and amenability to unlearning in quantum machine learning", see the [project repo](https://github.com/yutuer21/quantum-machine-unlearning).

Reference paper: https://arxiv.org/abs/2508.02422 (published in Nature Communications).

### Low Weight Pauli Propagation Simulation

For the simulation code and data for the work on low weight Pauli propagation in the context of variational quantum algorithms, see the [project repo](https://github.com/ZongliangLi/lwpp_init).

Reference paper: https://arxiv.org/abs/2508.06358 (published in PRR).

### Quantum Continual Learning

For the code implementation on the work of demonstrating plasticity in quantum continual learning, see the [project repo](https://github.com/sxzgroup/quantum-plasticity).

Reference paper: https://arxiv.org/abs/2511.17228 (published in PRX Quantum).

### More works

<details>
  <summary> More research works and code projects using TensorCircuit and TensorCircuit-NG (click for details) </summary>

- Neural Predictor based Quantum Architecture Search: https://arxiv.org/abs/2103.06524 (published in Machine Learning: Science and Technology).

- Quantum imaginary-time control for accelerating the ground-state preparation: https://arxiv.org/abs/2112.11782 (published in PRR).

- Efficient Quantum Simulation of Electron-Phonon Systems by Variational Basis State Encoder: https://arxiv.org/abs/2301.01442 (published in PRR).

- Variational Quantum Simulations of Finite-Temperature Dynamical Properties via Thermofield Dynamics: https://arxiv.org/abs/2206.05571.

- Understanding quantum machine learning also requires rethinking generalization: https://arxiv.org/abs/2306.13461 (published in Nature Communications).

- Decentralized Quantum Federated Learning for Metaverse: Analysis, Design and Implementation: https://arxiv.org/abs/2306.11297. Code: https://github.com/s222416822/BQFL.

- Non-IID quantum federated learning with one-shot communication complexity: https://arxiv.org/abs/2209.00768 (published in Quantum Machine Intelligence). Code: https://github.com/JasonZHM/quantum-fed-infer.

- Quantum generative adversarial imitation learning: https://doi.org/10.1088/1367-2630/acc605 (published in New Journal of Physics).

- GSQAS: Graph Self-supervised Quantum Architecture Search: https://arxiv.org/abs/2303.12381 (published in Physica A: Statistical Mechanics and its Applications).

- Practical advantage of quantum machine learning in ghost imaging: https://www.nature.com/articles/s42005-023-01290-1 (published in Communications Physics).

- Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic: https://arxiv.org/abs/2308.11616 (published in Quantum).

- Comparison of Quantum Simulators for Variational Quantum Search: A Benchmark Study: https://arxiv.org/abs/2309.05924.

- Statistical analysis of quantum state learning process in quantum neural networks: https://arxiv.org/abs/2309.14980 (published in NeurIPS).

- Generative quantum machine learning via denoising diffusion probabilistic models: https://arxiv.org/abs/2310.05866 (published in PRL).

- Exploring the topological sector optimization on quantum computers: https://arxiv.org/abs/2310.04291 (published in PRApplied).

- Google Summer of Code 2023 Projects (QML4HEP): https://github.com/ML4SCI/QMLHEP, https://github.com/Gopal-Dahale/qgnn-hep, https://github.com/salcc/QuantumTransformers.

- Universal imaginary-time critical dynamics on a quantum computer: https://arxiv.org/abs/2308.05408 (published in PRB).

- Non-Markovianity benefits quantum dynamics simulation: https://arxiv.org/abs/2311.17622.

- Variational post-selection for ground states and thermal states simulation: https://arxiv.org/abs/2402.07605 (published in QST).

- Subsystem information capacity in random circuits and Hamiltonian dynamics: https://arxiv.org/abs/2405.05076 (published in Quantum). Code implementation: https://github.com/sxzgroup/subsystem_information_capacity.

- Symmetry restoration and quantum Mpemba effect in symmetric random circuits: https://arxiv.org/abs/2403.08459 (published in PRL).

- Quantum Mpemba effects in many-body localization systems: https://arxiv.org/abs/2408.07750.

- Supersymmetry dynamics on Rydberg atom arrays: https://arxiv.org/abs/2410.21386 (published in PRB).

- Dynamic parameterized quantum circuits: expressive and barren-plateau free: https://arxiv.org/abs/2411.05760.

- Holographic deep thermalization: https://arxiv.org/abs/2411.03587 (published in Nature Communications).

- Quantum deep generative prior with programmable quantum circuits: https://www.nature.com/articles/s42005-024-01765-9 (published in Communications Physics).

- Symmetry Breaking Dynamics in Quantum Many-Body Systems: https://arxiv.org/abs/2501.13459 (published in CPL).

- Entanglement growth and information capacity in a quasiperiodic system with a single-particle mobility edge: https://arxiv.org/abs/2506.18076.

- Hilbert subspace imprint: a new mechanism for non-thermalization: https://arxiv.org/abs/2506.11922.

- A Neural-Guided Variational Quantum Algorithm for Efficient Sign Structure Learning in Hybrid Architectures: https://arxiv.org/abs/2507.07555.

- Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics: https://arxiv.org/abs/2509.01960 (published in PRB).

- Quantum Mpemba effect in long-ranged U(1)-symmetric random circuits: https://arxiv.org/abs/2512.06775 (published in PRB).

- A Qudit-native Framework for Discrete Time Crystals: https://arxiv.org/abs/2512.04577.

</details>

If you want to highlight your research work or projects here, feel free to add by opening PR.

## Users

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