{"id":13536235,"url":"https://github.com/unitaryfoundation/mitiq","last_synced_at":"2026-03-08T17:04:40.090Z","repository":{"id":37070788,"uuid":"236706881","full_name":"unitaryfoundation/mitiq","owner":"unitaryfoundation","description":"Mitiq is an open source toolkit for implementing error mitigation techniques on most current intermediate-scale quantum 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returned=1 errno=0 peeraddr=140.82.121.5:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["error-mitigation","quantum-computing","quantum-error-mitigation","quantum-programming"],"created_at":"2024-08-01T09:00:36.297Z","updated_at":"2026-03-08T17:04:40.081Z","avatar_url":"https://github.com/unitaryfoundation.png","language":"Python","readme":"# \u003ca href=\"https://github.com/unitaryfoundation/mitiq\"\u003e\u003cimg src=\"https://raw.githubusercontent.com/unitaryfoundation/mitiq/main/docs/source/img/mitiq-logo.png\" alt=\"Mitiq logo\" width=\"350\"/\u003e\u003c/a\u003e\n\n[![build](https://github.com/unitaryfoundation/mitiq/actions/workflows/build.yml/badge.svg?branch=main)](https://github.com/unitaryfoundation/mitiq/actions)\n[![Documentation Status](https://readthedocs.org/projects/mitiq/badge/?version=stable)](https://mitiq.readthedocs.io/en/stable/)\n[![codecov](https://codecov.io/gh/unitaryfoundation/mitiq/branch/main/graph/badge.svg)](https://codecov.io/gh/unitaryfoundation/mitiq)\n[![PyPI version](https://badge.fury.io/py/mitiq.svg)](https://badge.fury.io/py/mitiq)\n[![arXiv](https://img.shields.io/badge/arXiv-2009.04417-\u003cCOLOR\u003e.svg)](https://arxiv.org/abs/2009.04417)\n[![Downloads](https://static.pepy.tech/personalized-badge/mitiq?period=total\u0026units=international_system\u0026left_color=black\u0026right_color=green\u0026left_text=Downloads)](https://www.pepy.tech/projects/mitiq)\n[![License](https://img.shields.io/github/license/unitaryfoundation/mitiq)](https://github.com/unitaryfoundation/mitiq/blob/main/LICENSE)\n[![Repository](https://img.shields.io/badge/GitHub-5C5C5C.svg?logo=github)](https://github.com/unitaryfoundation/mitiq)\n[![Unitary Foundation](https://img.shields.io/badge/Supported%20By-Unitary%20Foundation-FFFF00.svg)](https://unitary.foundation)\n[![Discord Chat](https://img.shields.io/badge/dynamic/json?color=blue\u0026label=Discord\u0026query=approximate_presence_count\u0026suffix=%20online.\u0026url=https%3A%2F%2Fdiscord.com%2Fapi%2Finvites%2FJqVGmpkP96%3Fwith_counts%3Dtrue)](http://discord.unitary.foundation)\n\nMitiq [mitt • tick] is a Python toolkit for implementing error mitigation techniques on quantum computers.\n\nCurrent quantum computers are noisy due to interactions with the environment, imperfect gate applications, state preparation and measurement errors, etc.\nError mitigation seeks to reduce these effects at the software level by compiling quantum programs in clever ways.\n\nWant to know more? \n- Check out our\n[documentation](https://mitiq.readthedocs.io/en/stable/guide/guide.html).\n- For code, repo, or theory questions, especially those requiring more detailed responses, submit a [Discussion](https://github.com/unitaryfoundation/mitiq/discussions).\n- For casual or time sensitive questions, chat with mitiq developers on the `#mitiq` channel on [Discord](http://discord.unitary.foundation).\n- Contributions to Mitiq are eligible for compensation! More details [here](https://unitary.foundation/posts/2025_merit_systems_uf/), and all payouts can be found on [our wiki](https://github.com/unitaryfoundation/mitiq/wiki/Getting-paid-to-contribute-to-mitiq)!\n\n## Quickstart\n\n### Installation\n\n```bash\npip install mitiq\n```\n\n### Example\n\nDefine a function which takes a circuit as input and returns an expectation value you want to compute, then use Mitiq to mitigate errors.\n\n```python\nimport cirq\nfrom mitiq import zne, benchmarks\n\n\ndef execute(circuit, noise_level=0.005):\n    \"\"\"Returns Tr[ρ |0⟩⟨0|] where ρ is the state prepared by the circuit\n    with depolarizing noise.\"\"\"\n    noisy_circuit = circuit.with_noise(cirq.depolarize(p=noise_level))\n    return (\n        cirq.DensityMatrixSimulator()\n        .simulate(noisy_circuit)\n        .final_density_matrix[0, 0]\n        .real\n    )\n\n\ncircuit = benchmarks.generate_rb_circuits(n_qubits=1, num_cliffords=50)[0]\n\ntrue_value = execute(circuit, noise_level=0.0)      # Ideal quantum computer\nnoisy_value = execute(circuit)                      # Noisy quantum computer\nzne_value = zne.execute_with_zne(circuit, execute)  # Noisy quantum computer + Mitiq\n\nprint(f\"Error w/o  Mitiq: {abs((true_value - noisy_value) / true_value):.3f}\")\nprint(f\"Error w Mitiq:    {abs((true_value - zne_value) / true_value):.3f}\")\n```\n\nSample output:\n\n```\nError w/o  Mitiq: 0.264\nError w Mitiq:    0.073\n```\n\n### Calibration\n\nUnsure which error mitigation technique or parameters to use?\nTry out the calibration module demonstrated below to help find the best parameters for your particular backend!\n\n![](docs/source/img/calibration.gif)\n\nSee our [guides](https://mitiq.readthedocs.io/en/stable/guide/guide.html) and [examples](https://mitiq.readthedocs.io/en/stable/examples/examples.html) for more explanation, techniques, and benchmarks.\n\n## Quick Tour\n\n### Error mitigation techniques\nYou can check out currently available quantum error mitigation techniques by calling \n```python\nmitiq.qem_methods()\n```\n\n| Technique                                 | Documentation                                                | Mitiq module                                                              | Paper Reference(s)                                                                                                                                 |\n| ----------------------------------------- | ------------------------------------------------------------ | ------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------- |\n| Zero-noise extrapolation                  | [ZNE](https://mitiq.readthedocs.io/en/latest/guide/zne.html) | [`mitiq.zne`](https://github.com/unitaryfoundation/mitiq/tree/main/mitiq/zne) | [1611.09301](https://arxiv.org/abs/1611.09301)\u003cbr\u003e[1612.02058](https://arxiv.org/abs/1612.02058)\u003cbr\u003e[1805.04492](https://arxiv.org/abs/1805.04492) |\n| Probabilistic error cancellation          | [PEC](https://mitiq.readthedocs.io/en/latest/guide/pec.html) | [`mitiq.pec`](https://github.com/unitaryfoundation/mitiq/tree/main/mitiq/pec) | [1612.02058](https://arxiv.org/abs/1612.02058)\u003cbr\u003e[1712.09271](https://arxiv.org/abs/1712.09271)\u003cbr\u003e[1905.10135](https://arxiv.org/abs/1905.10135) |\n| (Variable-noise) Clifford data regression | [CDR](https://mitiq.readthedocs.io/en/latest/guide/cdr.html) | [`mitiq.cdr`](https://github.com/unitaryfoundation/mitiq/tree/main/mitiq/cdr) | [2005.10189](https://arxiv.org/abs/2005.10189)\u003cbr\u003e[2011.01157](https://arxiv.org/abs/2011.01157)                                                   |\n| Digital dynamical decoupling              | [DDD](https://mitiq.readthedocs.io/en/latest/guide/ddd.html) | [`mitiq.ddd`](https://github.com/unitaryfoundation/mitiq/tree/main/mitiq/ddd) | [9803057](https://arxiv.org/abs/quant-ph/9803057)\u003cbr\u003e[1807.08768](https://arxiv.org/abs/1807.08768)                                                |\n| Readout-error mitigation                  | [REM](https://mitiq.readthedocs.io/en/latest/guide/rem.html) | [`mitiq.rem`](https://github.com/unitaryfoundation/mitiq/tree/main/mitiq/rem) | [1907.08518](https://arxiv.org/abs/1907.08518) \u003cbr\u003e[2006.14044](https://arxiv.org/abs/2006.14044)\n| Quantum Subspace Expansion                  | [QSE](https://mitiq.readthedocs.io/en/stable/guide/qse.html) | [`mitiq.qse`](https://github.com/unitaryfoundation/mitiq/tree/main/mitiq/qse) | [1903.05786](https://arxiv.org/abs/1903.05786)|\n| Robust Shadow Estimation   🚧           | [RSE](https://mitiq.readthedocs.io/en/stable/guide/shadows.html)| [`mitiq.shadows`](https://github.com/unitaryfoundation/mitiq/tree/main/mitiq/shadows) | [2011.09636](https://arxiv.org/abs/2011.09636) \u003cbr\u003e [2002.08953](https://arxiv.org/abs/2002.08953)|\n| Layerwise Richardson Extrapolation  | [LRE](https://mitiq.readthedocs.io/en/stable/guide/lre.html) |  [`mitiq.lre`](https://github.com/unitaryfoundation/mitiq/tree/main/mitiq/lre) | [2402.04000](https://arxiv.org/abs/2402.04000) |\n| Probabilistic Error Amplification 🚧  | Coming soon |  `mitiq.pea` | [Nature](https://www.nature.com/articles/s41586-023-06096-3) |\n| Virtual Distillation 🚧  | Coming soon |  `mitiq.vd` | [APS](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.041036) |\n\n\u003e 🚧: Technique is currently a work in progress or is untested and may have some rough edges. If you try any of these techniques and have suggestions, please open an issue!\n\nIn addition, we also have Pauli Twirling which is a noise tailoring technique:\n\n\n| Noise-tailoring Technique                                 | Documentation                                                | Mitiq module                                                              | Paper Reference(s)                                                                                                                                 |\n| ----------------------------------------- | ------------------------------------------------------------ | ------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------- |\n| Pauli Twirling              | [PT](https://mitiq.readthedocs.io/en/latest/guide/pt.html)  | [`mitiq.pt`](https://github.com/unitaryfoundation/mitiq/tree/main/mitiq/pt) |  [1512.01098](https://arxiv.org/abs/1512.01098) |\n\n\nIf there is a technique you are looking for not listed here, please file a [feature request](https://github.com/unitaryfoundation/mitiq/issues/new?assignees=\u0026labels=feature-request\u0026template=feature_request.md\u0026title=).\n\n### Interface\n\nWe refer to any python quantum programming SDK you can write quantum circuits in as a _frontend_, and any quantum computer / simulator you can simulate circuits on as a _backend_.\n\n#### Supported frontends\n\n\n|                                                                   [Cirq](https://quantumai.google/cirq)                                                                    |                                     [Qiskit](https://www.ibm.com/quantum/qiskit)                                      |                                                      [pyQuil](https://github.com/rigetti/pyquil)                                                       |                                                            [Braket](https://github.com/aws/amazon-braket-sdk-python)                                                             |                                                                                  [PennyLane](https://pennylane.ai/)                                                                                     |                                          [Qibo](https://qibo.science/)                                                                                                   |                                                [OpenQASM 3](https://github.com/openqasm/openqasm)                                                 |\n|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:---------------------------------------------------------------------------------------------------------------------:|:------------------------------------------------------------------------------------------------------------------------------------------------------:|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|\n| \u003ca href=\"https://quantumai.google/cirq\"\u003e\u003cimg src=\"https://raw.githubusercontent.com/quantumlib/Cirq/main/docs/images/Cirq_logo_color.png\" alt=\"Cirq logo\" width=\"65\"/\u003e\u003c/a\u003e | \u003ca href=\"https://qiskit.org/\"\u003e\u003cimg src=\"https://raw.githubusercontent.com/unitaryfoundation/mitiq/main/docs/source/img/frontend-logos/qiskit-logo.png\" alt=\"Qiskit logo\" width=\"85\"/\u003e\u003c/a\u003e | \u003ca href=\"https://github.com/rigetti/pyquil\"\u003e\u003cimg src=\"https://www.rigetti.com/uploads/Logos/logo-rigetti-gray.jpg\" alt=\"Rigetti logo\" width=\"75\"/\u003e\u003c/a\u003e | \u003ca href=\"https://github.com/aws/amazon-braket-sdk-python\"\u003e\u003cimg src=\"https://a0.awsstatic.com/libra-css/images/logos/aws_logo_smile_1200x630.png\" alt=\"AWS logo\" width=\"75\"/\u003e\u003c/a\u003e | \u003ca href=\"https://pennylane.ai/\"\u003e\u003cimg src=\"https://raw.githubusercontent.com/PennyLaneAI/pennylane/c2f96705efd4570e8755e829b11cc869b4c2287d/doc/_static/logo.png\" alt=\"PennyLane logo\"  width=\"30\"/\u003e\u003c/a\u003e | \u003ca href=\"https://qibo.science/\"\u003e\u003cimg src=\"https://raw.githubusercontent.com/qiboteam/qibo/master/doc/source/_static/qibo_logo_dark.svg\" alt=\"Qibo logo\" width=\"60\"/\u003e\u003c/a\u003e | |\n\nYou can install Mitiq support for these frontends by specifying them during installation,  as optional extras, along with the main package.\nTo install Mitiq with one or more frontends, you can specify each frontend in square brackets as part of the installation command. \n\nFor example, to install Mitiq with support for Qiskit and Qibo:\n\n```bash\npip install mitiq[qiskit,qibo]\n```\n\n[Here](https://github.com/unitaryfoundation/mitiq/blob/main/INTEGRATIONS.txt) is an up-to-date list of supported frontends. \n\nNote: Currently, Cirq is a core requirement of Mitiq and is installed when you `pip install mitiq`.\n\n#### Supported backends\n\nYou can use Mitiq with any backend you have access to that can interface with supported frontends.\n\n### Citing Mitiq\n\nIf you use Mitiq in your research, please reference the [Mitiq whitepaper](https://quantum-journal.org/papers/q-2022-08-11-774/) using the bibtex entry found in [`CITATION.bib`](https://github.com/unitaryfoundation/mitiq/blob/main/CITATION.bib).\n\nA list of papers citing Mitiq can be found on [Google Scholar](https://scholar.google.com/scholar?cites=1985661232443186918) / [Semantic Scholar](https://api.semanticscholar.org/CorpusID:221555755?).\n\n## License\n\n[GNU GPL v.3.0.](https://github.com/unitaryfoundation/mitiq/blob/main/LICENSE)\n\n## Contributing\n\nWe welcome contributions to Mitiq including bug fixes, feature requests, etc.\nTo get started, check out our [contribution guidelines](https://mitiq.readthedocs.io/en/stable/toc_contributing.html) and/or [documentation guidelines](https://mitiq.readthedocs.io/en/stable/contributing_docs.html).\n\nContributions of all kinds are welcome!\n\n## Contributors ✨\n\nThank you to all of the [wonderful people](https://github.com/unitaryfoundation/mitiq/graphs/contributors) that have made this project possible.\nNon-code contributors are also much appreciated, and are listed here.\nThank you to\n\n- [@francespoblete](https://github.com/francespoblete) for much of Mitiq's design work/vision\n","funding_links":["https://github.com/sponsors/unitaryfoundation"],"categories":["Quantum Software Packages","Community","Python","Quantum compilers"],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Funitaryfoundation%2Fmitiq","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Funitaryfoundation%2Fmitiq","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Funitaryfoundation%2Fmitiq/lists"}