tensorcircuit-nightly

Name	tensorcircuit-nightly JSON
Version	1.2.1.dev20250712 JSON
	download
home_page	https://github.com/refraction-ray/tensorcircuit-dev
Summary	nightly release for tensorcircuit
upload_time	2025-07-12 12:49:15
maintainer	None
docs_url	None
author	TensorCircuit Authors
requires_python	None
license	None
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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, built upon tensornetwork engines, supporting for automatic differentiation, just-in-time compiling, hardware acceleration, and vectorized parallelism, 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, noisy, Clifford, approximate and analog cases. It also supports quantum hardware access and provides CPU/GPU/QPU hybrid deployment solutions.

TensorCircuit-NG is the actively maintained official version and a [fully compatible](https://tensorcircuit-ng.readthedocs.io/en/latest/faq.html#what-is-the-relation-between-tensorcircuit-and-tensorcircuit-ng) successor to TensorCircuit with more new features (stabilizer circuit and distributed simulation) and bug fixes (support latest `numpy>2` and `qiskit>1`).

## 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 80+ [example scripts](/examples) and 30+ [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 tensorcircuit-ng [deepwiki](https://deepwiki.com/tensorcircuit/tensorcircuit-ng) generated by LLM.

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.

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("tensorflow")
tc.set_dtype("complex128")
tc.set_contractor("greedy")
```

- 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 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
```

We also have [Docker support](/docker).

## 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 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**.

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

  - 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.

  - 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.

  </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 our software whitepaper 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)

which is also a good introduction to the software.

Research works citing TensorCircuit 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>
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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>
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      <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>
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      <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>
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      <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>
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      <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>
    </tr>
    <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>
  </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 and open-source projects that utilize 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).

### 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.

### 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.

### 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).

- Absence of barren plateaus in finite local-depth circuits with long-range entanglement: https://arxiv.org/abs/2311.01393 (published in PRL).

- 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. 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.

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

- Holographic deep thermalization: https://arxiv.org/abs/2411.03587.

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

</details>

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

## Users

Our users, developers, and partners:

<p align="center">
    <img width=90% src="docs/source/statics/user_logo.png">
</p>

            

Raw data

            {
    "_id": null,
    "home_page": "https://github.com/refraction-ray/tensorcircuit-dev",
    "name": "tensorcircuit-nightly",
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    "author": "TensorCircuit Authors",
    "author_email": "znfesnpbh.tc@gmail.com",
    "download_url": "https://files.pythonhosted.org/packages/de/cd/88b6351512368f8f8f5fe1fbad4a4db0680719458ba32584f9c7bfce7ba7/tensorcircuit_nightly-1.2.1.dev20250712.tar.gz",
    "platform": null,
    "description": "<p align=\"center\">\n  <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng\">\n    <img width=90% src=\"docs/source/statics/logong.png\">\n  </a>\n</p>\n\n<p align=\"center\">\n  <!-- tests (GitHub actions) -->\n  <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/actions/workflows/ci.yml\">\n    <img src=\"https://img.shields.io/github/actions/workflow/status/tensorcircuit/tensorcircuit-ng/ci.yml?branch=master\" />\n  </a>\n  <!-- docs -->\n  <a href=\"https://tensorcircuit-ng.readthedocs.io/\">\n    <img src=\"https://img.shields.io/badge/docs-link-green.svg?logo=read-the-docs\"/>\n  </a>\n  <!-- PyPI -->\n  <a href=\"https://pypi.org/project/tensorcircuit-ng/\">\n    <img src=\"https://img.shields.io/pypi/v/tensorcircuit-ng.svg?logo=pypi\"/>\n  </a>\n  <!-- License -->\n  <a href=\"./LICENSE\">\n    <img src=\"https://img.shields.io/badge/license-Apache%202.0-blue.svg?logo=apache\"/>\n  </a>\n</p>\n\n<p align=\"center\"> English | <a href=\"README_cn.md\"> \u7b80\u4f53\u4e2d\u6587 </a></p>\n\nTensorCircuit-NG is the next-generation open-source high-performance quantum software framework, built upon tensornetwork engines, supporting for automatic differentiation, just-in-time compiling, hardware acceleration, and vectorized parallelism, 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.\n\nTensorCircuit-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, noisy, Clifford, approximate and analog cases. It also supports quantum hardware access and provides CPU/GPU/QPU hybrid deployment solutions.\n\nTensorCircuit-NG is the actively maintained official version and a [fully compatible](https://tensorcircuit-ng.readthedocs.io/en/latest/faq.html#what-is-the-relation-between-tensorcircuit-and-tensorcircuit-ng) successor to TensorCircuit with more new features (stabilizer circuit and distributed simulation) and bug fixes (support latest `numpy>2` and `qiskit>1`).\n\n## Getting Started\n\nPlease begin with [Quick Start](/docs/source/quickstart.rst) in the [full documentation](https://tensorcircuit-ng.readthedocs.io/).\n\nFor more information on software usage, sota algorithm implementation and engineer paradigm demonstration, please refer to 80+ [example scripts](/examples) and 30+ [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 tensorcircuit-ng [deepwiki](https://deepwiki.com/tensorcircuit/tensorcircuit-ng) generated by LLM.\n\nFor 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.\n\nThe following are some minimal demos.\n\n- Circuit construction:\n\n```python\nimport tensorcircuit as tc\nc = tc.Circuit(2)\nc.H(0)\nc.CNOT(0,1)\nc.rx(1, theta=0.2)\nprint(c.wavefunction())\nprint(c.expectation_ps(z=[0, 1]))\nprint(c.sample(allow_state=True, batch=1024, format=\"count_dict_bin\"))\n```\n\n- Runtime behavior customization:\n\n```python\ntc.set_backend(\"tensorflow\")\ntc.set_dtype(\"complex128\")\ntc.set_contractor(\"greedy\")\n```\n\n- Automatic differentiation with jit:\n\n```python\ndef forward(theta):\n    c = tc.Circuit(2)\n    c.R(0, theta=theta, alpha=0.5, phi=0.8)\n    return tc.backend.real(c.expectation((tc.gates.z(), [0])))\n\ng = tc.backend.grad(forward)\ng = tc.backend.jit(g)\ntheta = tc.array_to_tensor(1.0)\nprint(g(theta))\n```\n\n<details>\n  <summary> More highlight features for TensorCircuit (click for details) </summary>\n\n- Sparse Hamiltonian generation and expectation evaluation:\n\n```python\nn = 6\npauli_structures = []\nweights = []\nfor i in range(n):\n    pauli_structures.append(tc.quantum.xyz2ps({\"z\": [i, (i + 1) % n]}, n=n))\n    weights.append(1.0)\nfor i in range(n):\n    pauli_structures.append(tc.quantum.xyz2ps({\"x\": [i]}, n=n))\n    weights.append(-1.0)\nh = tc.quantum.PauliStringSum2COO(pauli_structures, weights)\nprint(h)\n# BCOO(complex64[64, 64], nse=448)\nc = tc.Circuit(n)\nc.h(range(n))\nenergy = tc.templates.measurements.operator_expectation(c, h)\n# -6\n```\n\n- Large-scale simulation with tensor network engine\n\n```python\n# tc.set_contractor(\"cotengra-30-10\")\nn=500\nc = tc.Circuit(n)\nc.h(0)\nc.cx(range(n-1), range(1, n))\nc.expectation_ps(z=[0, n-1], reuse=False)\n```\n\n- Density matrix simulator and quantum info quantities\n\n```python\nc = tc.DMCircuit(2)\nc.h(0)\nc.cx(0, 1)\nc.depolarizing(1, px=0.1, py=0.1, pz=0.1)\ndm = c.state()\nprint(tc.quantum.entropy(dm))\nprint(tc.quantum.entanglement_entropy(dm, [0]))\nprint(tc.quantum.entanglement_negativity(dm, [0]))\nprint(tc.quantum.log_negativity(dm, [0]))\n```\n\n</details>\n\n## Install\n\nThe package is written in pure Python and can be obtained via pip as:\n\n```python\npip install tensorcircuit-ng\n```\n\nWe recommend you install this package with tensorflow also installed as:\n\n```python\npip install \"tensorcircuit-ng[tensorflow]\"\n```\n\nOther optional dependencies include `[torch]`, `[jax]`, `[qiskit]` and `[cloud]`.\n\nTry nightly build for the newest features:\n\n```python\npip install tensorcircuit-nightly\n```\n\nWe also have [Docker support](/docker).\n\n## Advantages\n\n- Tensor network simulation engine based\n\n- JIT, AD, vectorized parallelism compatible\n\n- GPU support, QPU access support, hybrid deployment support\n\n- HPC native, distributed simulation enabled, multiple devices/hosts support\n\n- Efficiency\n\n  - Time: 10 to 10^6+ times acceleration compared to TensorFlow Quantum, Pennylane or Qiskit\n\n  - Space: 600+ qubits 1D VQE workflow (converged energy inaccuracy: < 1%)\n\n- Elegance\n\n  - Flexibility: customized contraction, multiple ML backend/interface choices, multiple dtype precisions, multiple QPU providers\n\n  - API design: quantum for humans, less code, more power\n\n- Batteries included\n\n  <details>\n  <summary> Tons of amazing features and built in tools for research (click for details) </summary>\n\n  - Support **super large circuit simulation** using tensor network engine.\n\n  - Support **noisy simulation** with both Monte Carlo and density matrix (tensor network powered) modes.\n\n  - Support **stabilizer circuit simulation** with stim backend\n\n  - Support **approximate simulation** with MPS-TEBD modes.\n\n  - Support **analog/digital hybrid simulation** (time dependent Hamiltonian evolution, **pulse** level simulation) with neural ode modes.\n\n  - Support **Fermion Gaussian state** simulation with expectation, entanglement, measurement, ground state, real and imaginary time evolution.\n\n  - Support **qudits simulation**.\n\n  - Support **parallel** quantum circuit evaluation across **multiple GPUs**.\n\n  - Highly customizable **noise model** with gate error and scalable readout error.\n\n  - Support for **non-unitary** gate and post-selection simulation.\n\n  - Support **real quantum devices access** from different providers.\n\n  - **Scalable readout error mitigation** native to both bitstring and expectation level with automatic qubit mapping consideration.\n\n  - **Advanced quantum error mitigation methods** and pipelines such as ZNE, DD, RC, etc.\n\n  - Support **MPS/MPO** as representations for input states, quantum gates and observables to be measured.\n\n  - Support **vectorized parallelism** on circuit inputs, circuit parameters, circuit structures, circuit measurements and these vectorization can be nested.\n\n  - Gradients can be obtained with both **automatic differenation** and parameter shift (vmap accelerated) modes.\n\n  - **Machine learning interface/layer/model** abstraction in both TensorFlow, PyTorch and Jax for both numerical simulation and real QPU experiments.\n\n  - Circuit sampling supports both final state sampling and perfect sampling from tensor networks.\n\n  - Light cone reduction support for local expectation calculation.\n\n  - Highly customizable tensor network contraction path finder with opteinsum and cotengra interface.\n\n  - Observables are supported in measurement, sparse matrix, dense matrix and MPO format.\n\n  - Super fast weighted sum Pauli string Hamiltonian matrix generation.\n\n  - Reusable common circuit/measurement/problem templates and patterns.\n\n  - Jittable classical shadow infrastructures.\n\n  - SOTA quantum algorithm and model implementations.\n\n  - 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.\n\n  </details>\n\n## Contributing\n\n### Status\n\nThis 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.\n\n### Citation\n\nIf this project helps in your research, please cite our software whitepaper to acknowledge the work put into the development of TensorCircuit-NG.\n\n[TensorCircuit: a Quantum Software Framework for the NISQ Era](https://quantum-journal.org/papers/q-2023-02-02-912/) (published in Quantum)\n\nwhich is also a good introduction to the software.\n\nResearch works citing TensorCircuit can be highlighted in [Research and Applications section](https://github.com/tensorcircuit/tensorcircuit-ng#research-and-applications).\n\n### Guidelines\n\nFor contribution guidelines and notes, see [CONTRIBUTING](/CONTRIBUTING.md).\n\nWe 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.\n\n### License\n\nTensorCircuit-NG is open source, released under the Apache License, Version 2.0.\n\n### Contributors\n\n<!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->\n<!-- prettier-ignore-start -->\n<!-- markdownlint-disable -->\n<table>\n  <tbody>\n    <tr>\n      <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\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=refraction-ray\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#example-refraction-ray\" title=\"Examples\">\ud83d\udca1</a> <a href=\"#ideas-refraction-ray\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a> <a href=\"#infra-refraction-ray\" title=\"Infrastructure (Hosting, Build-Tools, etc)\">\ud83d\ude87</a> <a href=\"#maintenance-refraction-ray\" title=\"Maintenance\">\ud83d\udea7</a> <a href=\"#research-refraction-ray\" title=\"Research\">\ud83d\udd2c</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/pulls?q=is%3Apr+reviewed-by%3Arefraction-ray\" title=\"Reviewed Pull Requests\">\ud83d\udc40</a> <a href=\"#translation-refraction-ray\" title=\"Translation\">\ud83c\udf0d</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=refraction-ray\" title=\"Tests\">\u26a0\ufe0f</a> <a href=\"#tutorial-refraction-ray\" title=\"Tutorials\">\u2705</a> <a href=\"#talk-refraction-ray\" title=\"Talks\">\ud83d\udce2</a> <a href=\"#question-refraction-ray\" title=\"Answering Questions\">\ud83d\udcac</a> <a href=\"#financial-refraction-ray\" title=\"Financial\">\ud83d\udcb5</a></td>\n      <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\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=yutuer21\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#example-yutuer21\" title=\"Examples\">\ud83d\udca1</a> <a href=\"#ideas-yutuer21\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a> <a href=\"#research-yutuer21\" title=\"Research\">\ud83d\udd2c</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=yutuer21\" title=\"Tests\">\u26a0\ufe0f</a> <a href=\"#tutorial-yutuer21\" title=\"Tutorials\">\u2705</a> <a href=\"#talk-yutuer21\" title=\"Talks\">\ud83d\udce2</a></td>\n      <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\">\ud83d\udcbb</a> <a href=\"#example-xptree\" title=\"Examples\">\ud83d\udca1</a> <a href=\"#ideas-xptree\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a> <a href=\"#research-xptree\" title=\"Research\">\ud83d\udd2c</a></td>\n      <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\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=liwt31\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#ideas-liwt31\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a> <a href=\"#research-liwt31\" title=\"Research\">\ud83d\udd2c</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=liwt31\" title=\"Tests\">\u26a0\ufe0f</a> <a href=\"#talk-liwt31\" title=\"Talks\">\ud83d\udce2</a></td>\n      <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\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=SUSYUSTC\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#example-SUSYUSTC\" title=\"Examples\">\ud83d\udca1</a> <a href=\"#ideas-SUSYUSTC\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a> <a href=\"#research-SUSYUSTC\" title=\"Research\">\ud83d\udd2c</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=SUSYUSTC\" title=\"Tests\">\u26a0\ufe0f</a></td>\n      <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\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Zhouquan-Wan\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#example-Zhouquan-Wan\" title=\"Examples\">\ud83d\udca1</a> <a href=\"#ideas-Zhouquan-Wan\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a> <a href=\"#research-Zhouquan-Wan\" title=\"Research\">\ud83d\udd2c</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=Zhouquan-Wan\" title=\"Tests\">\u26a0\ufe0f</a> <a href=\"#tutorial-Zhouquan-Wan\" title=\"Tutorials\">\u2705</a></td>\n    </tr>\n    <tr>\n      <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\">\ud83d\udca1</a> <a href=\"#research-ls-iastu\" title=\"Research\">\ud83d\udd2c</a> <a href=\"#tutorial-ls-iastu\" title=\"Tutorials\">\u2705</a></td>\n      <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\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=YHPeter\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#infra-YHPeter\" title=\"Infrastructure (Hosting, Build-Tools, etc)\">\ud83d\ude87</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=YHPeter\" title=\"Tests\">\u26a0\ufe0f</a> <a href=\"#tutorial-YHPeter\" title=\"Tutorials\">\u2705</a></td>\n      <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\">\ud83d\udcd6</a> <a href=\"#translation-SexyCarrots\" title=\"Translation\">\ud83c\udf0d</a> <a href=\"#tutorial-SexyCarrots\" title=\"Tutorials\">\u2705</a></td>\n      <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\">\u2705</a> <a href=\"#translation-JachyMeow\" title=\"Translation\">\ud83c\udf0d</a></td>\n      <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\">\ud83c\udfa8</a></td>\n      <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\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=erertertet\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=erertertet\" title=\"Tests\">\u26a0\ufe0f</a></td>\n    </tr>\n    <tr>\n      <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\">\u2705</a></td>\n      <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\">\ud83d\udcd6</a> <a href=\"#translation-MarkSong535\" title=\"Translation\">\ud83c\udf0d</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=MarkSong535\" title=\"Code\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=MarkSong535\" title=\"Tests\">\u26a0\ufe0f</a></td>\n      <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\">\ud83d\udcd6</a></td>\n      <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\">\u26a0\ufe0f</a></td>\n      <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\">\ud83d\udcd6</a> <a href=\"#ideas-JAllcock\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a> <a href=\"#talk-JAllcock\" title=\"Talks\">\ud83d\udce2</a></td>\n      <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\">\ud83d\udcd6</a></td>\n    </tr>\n    <tr>\n      <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=\"\u9690\u516c\u89c2\u9c7c\"/><br /><sub><b>\u9690\u516c\u89c2\u9c7c</b></sub></a><br /><a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=eurethia\" title=\"Code\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=eurethia\" title=\"Tests\">\u26a0\ufe0f</a></td>\n      <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\">\ud83d\udca1</a></td>\n      <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\">\u2705</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=FelixXu35\" title=\"Code\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=FelixXu35\" title=\"Tests\">\u26a0\ufe0f</a></td>\n      <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\">\ud83d\udcd6</a></td>\n      <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\">\u2705</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=PeilinZHENG\" title=\"Code\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=PeilinZHENG\" title=\"Tests\">\u26a0\ufe0f</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=PeilinZHENG\" title=\"Documentation\">\ud83d\udcd6</a></td>\n      <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\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=EmilianoG-byte\" title=\"Tests\">\u26a0\ufe0f</a></td>\n    </tr>\n    <tr>\n      <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\">\ud83d\udcbb</a></td>\n      <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\">\ud83d\udca1</a></td>\n      <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\">\ud83d\udcbb</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=king-p3nguin\" title=\"Tests\">\u26a0\ufe0f</a> <a href=\"https://github.com/tensorcircuit/tensorcircuit-ng/commits?author=king-p3nguin\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#example-king-p3nguin\" title=\"Examples\">\ud83d\udca1</a></td>\n      <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\">\ud83d\udca1</a></td>\n      <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\">\ud83d\udca1</a></td>\n      <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\">\ud83d\udcbb</a></td>\n    </tr>\n  </tbody>\n</table>\n\n<!-- markdownlint-restore -->\n<!-- prettier-ignore-end -->\n\n<!-- ALL-CONTRIBUTORS-LIST:END -->\n<!-- prettier-ignore-start -->\n<!-- markdownlint-disable -->\n\n<!-- markdownlint-restore -->\n<!-- prettier-ignore-end -->\n\n<!-- ALL-CONTRIBUTORS-LIST:END -->\n\n## Research and Applications\n\nTensorCircuit-NG is a powerful framework for driving research and applications in quantum computing. Below are examples of published academic works and open-source projects that utilize TensorCircuit-NG.\n\n### DQAS\n\nFor the application of Differentiable Quantum Architecture Search, see [applications](/tensorcircuit/applications).\n\nReference paper: https://arxiv.org/abs/2010.08561 (published in QST).\n\n### VQNHE\n\nFor the application of Variational Quantum-Neural Hybrid Eigensolver, see [applications](/tensorcircuit/applications).\n\nReference paper: https://arxiv.org/abs/2106.05105 (published in PRL) and https://arxiv.org/abs/2112.10380 (published in AQT).\n\n### VQEX-MBL\n\nFor the application of VQEX on MBL phase identification, see the [tutorial](/docs/source/tutorials/vqex_mbl.ipynb).\n\nReference paper: https://arxiv.org/abs/2111.13719 (published in PRB).\n\n### Stark-DTC\n\nFor the numerical demosntration of discrete time crystal enabled by Stark many-body localization, see the Floquet simulation [demo](/examples/timeevolution_trotter.py).\n\nReference paper: https://arxiv.org/abs/2208.02866 (published in PRL).\n\n### RA-Training\n\nFor 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).\n\nReference paper: https://arxiv.org/abs/2303.08154 (published in PRR as a Letter).\n\n### TenCirChem\n\n[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).\n\nReference paper: https://arxiv.org/abs/2303.10825 (published in JCTC).\n\n### EMQAOA-DARBO\n\nFor the numerical simulation and hardware experiments with error mitigation on QAOA, see the [project repo](https://github.com/sherrylixuecheng/EMQAOA-DARBO).\n\nReference paper: https://arxiv.org/abs/2303.14877 (published in Communications Physics).\n\n### NN-VQA\n\nFor the setup and simulation code of neural network encoded variational quantum eigensolver, see the [demo](/docs/source/tutorials/nnvqe.ipynb).\n\nReference paper: https://arxiv.org/abs/2308.01068 (published in PRApplied).\n\n### Effective temperature in ansatzes\n\nFor 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).\n\nReference paper: https://arxiv.org/abs/2411.18921.\n\n### A Unified Variational Framework for Quantum Excited States\n\nFor the simulation code and data for variational optimization of simutaneous excited states, see the [project repo](https://github.com/sxzgroup/quantum_excited_state).\n\nReference paper: https://arxiv.org/abs/2504.21459.\n\n### More works\n\n<details>\n  <summary> More research works and code projects using TensorCircuit and TensorCircuit-NG (click for details) </summary>\n\n- Neural Predictor based Quantum Architecture Search: https://arxiv.org/abs/2103.06524 (published in Machine Learning: Science and Technology).\n\n- Quantum imaginary-time control for accelerating the ground-state preparation: https://arxiv.org/abs/2112.11782 (published in PRR).\n\n- Efficient Quantum Simulation of Electron-Phonon Systems by Variational Basis State Encoder: https://arxiv.org/abs/2301.01442 (published in PRR).\n\n- Variational Quantum Simulations of Finite-Temperature Dynamical Properties via Thermofield Dynamics: https://arxiv.org/abs/2206.05571.\n\n- Understanding quantum machine learning also requires rethinking generalization: https://arxiv.org/abs/2306.13461 (published in Nature Communications).\n\n- Decentralized Quantum Federated Learning for Metaverse: Analysis, Design and Implementation: https://arxiv.org/abs/2306.11297. Code: https://github.com/s222416822/BQFL.\n\n- 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.\n\n- Quantum generative adversarial imitation learning: https://doi.org/10.1088/1367-2630/acc605 (published in New Journal of Physics).\n\n- GSQAS: Graph Self-supervised Quantum Architecture Search: https://arxiv.org/abs/2303.12381 (published in Physica A: Statistical Mechanics and its Applications).\n\n- Practical advantage of quantum machine learning in ghost imaging: https://www.nature.com/articles/s42005-023-01290-1 (published in Communications Physics).\n\n- Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic: https://arxiv.org/abs/2308.11616 (published in Quantum).\n\n- Comparison of Quantum Simulators for Variational Quantum Search: A Benchmark Study: https://arxiv.org/abs/2309.05924.\n\n- Statistical analysis of quantum state learning process in quantum neural networks: https://arxiv.org/abs/2309.14980 (published in NeurIPS).\n\n- Generative quantum machine learning via denoising diffusion probabilistic models: https://arxiv.org/abs/2310.05866 (published in PRL).\n\n- Exploring the topological sector optimization on quantum computers: https://arxiv.org/abs/2310.04291 (published in PRApplied).\n\n- Google Summer of Code 2023 Projects (QML4HEP): https://github.com/ML4SCI/QMLHEP, https://github.com/Gopal-Dahale/qgnn-hep, https://github.com/salcc/QuantumTransformers.\n\n- Universal imaginary-time critical dynamics on a quantum computer: https://arxiv.org/abs/2308.05408 (published in PRB).\n\n- Absence of barren plateaus in finite local-depth circuits with long-range entanglement: https://arxiv.org/abs/2311.01393 (published in PRL).\n\n- Non-Markovianity benefits quantum dynamics simulation: https://arxiv.org/abs/2311.17622.\n\n- Variational post-selection for ground states and thermal states simulation: https://arxiv.org/abs/2402.07605 (published in QST).\n\n- Subsystem information capacity in random circuits and Hamiltonian dynamics: https://arxiv.org/abs/2405.05076. Code implementation: https://github.com/sxzgroup/subsystem_information_capacity.\n\n- Symmetry restoration and quantum Mpemba effect in symmetric random circuits: https://arxiv.org/abs/2403.08459 (published in PRL).\n\n- Quantum Mpemba effects in many-body localization systems: https://arxiv.org/abs/2408.07750.\n\n- Supersymmetry dynamics on Rydberg atom arrays: https://arxiv.org/abs/2410.21386.\n\n- Dynamic parameterized quantum circuits: expressive and barren-plateau free: https://arxiv.org/abs/2411.05760.\n\n- Holographic deep thermalization: https://arxiv.org/abs/2411.03587.\n\n- Quantum deep generative prior with programmable quantum circuits: https://www.nature.com/articles/s42005-024-01765-9 (published in Communications Physics).\n\n</details>\n\nIf you want to highlight your research work or projects here, feel free to add by opening PR.\n\n## Users\n\nOur users, developers, and partners:\n\n<p align=\"center\">\n    <img width=90% src=\"docs/source/statics/user_logo.png\">\n</p>\n",
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