tensorcircuit-ng 1.5.0
High performance unified quantum computing framework for the NISQ era
Requires Python: >=3.9

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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, 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`), and fermionic (`FGSCircuit`) cases. It also supports quantum hardware access and provides CPU/GPU/QPU hybrid deployment solutions.

TensorCircuit-NG is the only 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, qudit circuit, analog circuit, multi-GPU distributed simulation, etc.) 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 100+ [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) 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.

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 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
```

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** for tensor network and MPS approximation modes.

  - 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.

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

  - 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-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 -->
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      <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>
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      <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>
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      <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>
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  </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 (100+ in total) 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).

### 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.

### 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.

### 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.

### 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.

### 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.

- 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.

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

- 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

Our users, developers, and partners:

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