https://github.com/unitaryfoundation/mitiq
Mitiq is an open source toolkit for implementing error mitigation techniques on most current intermediate-scale quantum computers.
https://github.com/unitaryfoundation/mitiq
error-mitigation quantum-computing quantum-error-mitigation quantum-programming
Last synced: 4 days ago
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Mitiq is an open source toolkit for implementing error mitigation techniques on most current intermediate-scale quantum computers.
- Host: GitHub
- URL: https://github.com/unitaryfoundation/mitiq
- Owner: unitaryfoundation
- License: gpl-3.0
- Created: 2020-01-28T10:14:19.000Z (about 6 years ago)
- Default Branch: main
- Last Pushed: 2026-02-20T14:49:32.000Z (20 days ago)
- Last Synced: 2026-02-20T18:55:51.675Z (20 days ago)
- Topics: error-mitigation, quantum-computing, quantum-error-mitigation, quantum-programming
- Language: Python
- Homepage: https://mitiq.readthedocs.io
- Size: 65.2 MB
- Stars: 416
- Watchers: 11
- Forks: 198
- Open Issues: 112
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- Funding: .github/FUNDING.yml
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.bib
- Security: SECURITY.md
Awesome Lists containing this project
- quantum-awesome - https://github.com/unitaryfund/mitiq
- awesome-quantum-software - Mitiq - Cross-platform, quantum error mitigation toolkit and compiler from [Unitary Foundation](https://unitary.foundation/). (Quantum compilers)
README
# 
[](https://github.com/unitaryfoundation/mitiq/actions)
[](https://mitiq.readthedocs.io/en/stable/)
[](https://codecov.io/gh/unitaryfoundation/mitiq)
[](https://badge.fury.io/py/mitiq)
[](https://arxiv.org/abs/2009.04417)
[](https://www.pepy.tech/projects/mitiq)
[](https://github.com/unitaryfoundation/mitiq/blob/main/LICENSE)
[](https://github.com/unitaryfoundation/mitiq)
[](https://unitary.foundation)
[](http://discord.unitary.foundation)
Mitiq [mitt • tick] is a Python toolkit for implementing error mitigation techniques on quantum computers.
Current quantum computers are noisy due to interactions with the environment, imperfect gate applications, state preparation and measurement errors, etc.
Error mitigation seeks to reduce these effects at the software level by compiling quantum programs in clever ways.
Want to know more?
- Check out our
[documentation](https://mitiq.readthedocs.io/en/stable/guide/guide.html).
- For code, repo, or theory questions, especially those requiring more detailed responses, submit a [Discussion](https://github.com/unitaryfoundation/mitiq/discussions).
- For casual or time sensitive questions, chat with mitiq developers on the `#mitiq` channel on [Discord](http://discord.unitary.foundation).
- 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)!
## Quickstart
### Installation
```bash
pip install mitiq
```
### Example
Define a function which takes a circuit as input and returns an expectation value you want to compute, then use Mitiq to mitigate errors.
```python
import cirq
from mitiq import zne, benchmarks
def execute(circuit, noise_level=0.005):
"""Returns Tr[ρ |0⟩⟨0|] where ρ is the state prepared by the circuit
with depolarizing noise."""
noisy_circuit = circuit.with_noise(cirq.depolarize(p=noise_level))
return (
cirq.DensityMatrixSimulator()
.simulate(noisy_circuit)
.final_density_matrix[0, 0]
.real
)
circuit = benchmarks.generate_rb_circuits(n_qubits=1, num_cliffords=50)[0]
true_value = execute(circuit, noise_level=0.0) # Ideal quantum computer
noisy_value = execute(circuit) # Noisy quantum computer
zne_value = zne.execute_with_zne(circuit, execute) # Noisy quantum computer + Mitiq
print(f"Error w/o Mitiq: {abs((true_value - noisy_value) / true_value):.3f}")
print(f"Error w Mitiq: {abs((true_value - zne_value) / true_value):.3f}")
```
Sample output:
```
Error w/o Mitiq: 0.264
Error w Mitiq: 0.073
```
### Calibration
Unsure which error mitigation technique or parameters to use?
Try out the calibration module demonstrated below to help find the best parameters for your particular backend!
See 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.
## Quick Tour
### Error mitigation techniques
You can check out currently available quantum error mitigation techniques by calling
```python
mitiq.qem_methods()
```
| Technique | Documentation | Mitiq module | Paper Reference(s) |
| ----------------------------------------- | ------------------------------------------------------------ | ------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------- |
| 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)
[1612.02058](https://arxiv.org/abs/1612.02058)
[1805.04492](https://arxiv.org/abs/1805.04492) |
| 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)
[1712.09271](https://arxiv.org/abs/1712.09271)
[1905.10135](https://arxiv.org/abs/1905.10135) |
| (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)
[2011.01157](https://arxiv.org/abs/2011.01157) |
| 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)
[1807.08768](https://arxiv.org/abs/1807.08768) |
| 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)
[2006.14044](https://arxiv.org/abs/2006.14044)
| 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)|
| 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)
[2002.08953](https://arxiv.org/abs/2002.08953)|
| 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) |
| Probabilistic Error Amplification 🚧 | Coming soon | `mitiq.pea` | [Nature](https://www.nature.com/articles/s41586-023-06096-3) |
| Virtual Distillation 🚧 | Coming soon | `mitiq.vd` | [APS](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.041036) |
> 🚧: 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!
In addition, we also have Pauli Twirling which is a noise tailoring technique:
| Noise-tailoring Technique | Documentation | Mitiq module | Paper Reference(s) |
| ----------------------------------------- | ------------------------------------------------------------ | ------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------- |
| 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) |
If there is a technique you are looking for not listed here, please file a [feature request](https://github.com/unitaryfoundation/mitiq/issues/new?assignees=&labels=feature-request&template=feature_request.md&title=).
### Interface
We 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_.
#### Supported frontends
| [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) |
|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:---------------------------------------------------------------------------------------------------------------------:|:------------------------------------------------------------------------------------------------------------------------------------------------------:|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|
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You can install Mitiq support for these frontends by specifying them during installation, as optional extras, along with the main package.
To install Mitiq with one or more frontends, you can specify each frontend in square brackets as part of the installation command.
For example, to install Mitiq with support for Qiskit and Qibo:
```bash
pip install mitiq[qiskit,qibo]
```
[Here](https://github.com/unitaryfoundation/mitiq/blob/main/INTEGRATIONS.txt) is an up-to-date list of supported frontends.
Note: Currently, Cirq is a core requirement of Mitiq and is installed when you `pip install mitiq`.
#### Supported backends
You can use Mitiq with any backend you have access to that can interface with supported frontends.
### Citing Mitiq
If 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).
A 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?).
## License
[GNU GPL v.3.0.](https://github.com/unitaryfoundation/mitiq/blob/main/LICENSE)
## Contributing
We welcome contributions to Mitiq including bug fixes, feature requests, etc.
To 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).
Contributions of all kinds are welcome!
## Contributors ✨
Thank you to all of the [wonderful people](https://github.com/unitaryfoundation/mitiq/graphs/contributors) that have made this project possible.
Non-code contributors are also much appreciated, and are listed here.
Thank you to
- [@francespoblete](https://github.com/francespoblete) for much of Mitiq's design work/vision