Mitiq 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. - To see what's in store for Mitiq, look at our roadmap in the wiki. - For code, repo, or theory questions, especially those requiring more detailed responses, submit a Discussion. - For casual or time sensitive questions, chat with us on Discord. - Join our weekly community call on Discord (public agenda).

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, noiselevel=0.005): """Returns Tr[ρ |0⟩⟨0|] where ρ is the state prepared by the circuit with depolarizing noise.""" noisycircuit = circuit.withnoise(cirq.depolarize(p=noiselevel)) return ( cirq.DensityMatrixSimulator() .simulate(noisycircuit) .finaldensity_matrix[0, 0] .real )

circuit = benchmarks.generaterbcircuits(nqubits=1, numcliffords=50)[0]

truevalue = execute(circuit, noiselevel=0.0) # Ideal quantum computer noisyvalue = execute(circuit) # Noisy quantum computer znevalue = zne.executewithzne(circuit, execute) # Noisy quantum computer + Mitiq

print(f"Error w/o Mitiq: {abs((truevalue - noisyvalue) / truevalue):.3f}") print(f"Error w Mitiq: {abs((truevalue - znevalue) / truevalue):.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 and examples 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 | mitiq.zne | 1611.09301
1612.02058
1805.04492 | | Probabilistic error cancellation | PEC | mitiq.pec | 1612.02058
1712.09271
1905.10135 | | (Variable-noise) Clifford data regression | CDR | mitiq.cdr | 2005.10189
2011.01157 | | Digital dynamical decoupling | DDD | mitiq.ddd | 9803057
1807.08768 | | Readout-error mitigation | REM | mitiq.rem | 1907.08518
2006.14044 | Quantum Subspace Expansion | QSE | mitiq.qse | 1903.05786| | Robust Shadow Estimation 🚧 | RSE| mitiq.shadows | 2011.09636
2002.08953| | Layerwise Richardson Extrapolation | LRE | mitiq.lre | 2402.04000 | | Probabilistic Error Amplification 🚧 | Coming soon | mitiq.pea | Nature | | Virtual Distillation 🚧 | Coming soon | mitiq.vd | APS |

In addition, we also have a noise tailoring technique currently available with limited functionality:

| Noise-tailoring Technique | Documentation | Mitiq module | Paper Reference(s) | | ----------------------------------------- | ------------------------------------------------------------ | ------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------- | | Pauli Twirling 🚧 | PT | mitiq.pt | 1512.01098 |

🚧: 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!

See our roadmap for additional candidate techniques to implement. If there is a technique you are looking for, please file a feature request.

Interface

We refer to any programming language you can write quantum circuits in as a frontend, and any quantum computer / simulator you can simulate circuits in as a backend.

Supported frontends

| Cirq | Qiskit | pyQuil | Braket | PennyLane | Qibo | |:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:---------------------------------------------------------------------------------------------------------------------:|:------------------------------------------------------------------------------------------------------------------------------------------------------:|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------:|:------------------------------------------------------------------------------------------------------------------------------------------------------------------------:| | | | | | | |

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 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 (even without the optional [cirq])

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 using the bibtex entry found in CITATION.bib.

A list of papers citing Mitiq can be found on Google Scholar / Semantic Scholar.

License

GNU GPL v.3.0.

Contributing

We welcome contributions to Mitiq including bug fixes, feature requests, etc. To get started, check out our contribution guidelines and/or documentation guidelines.

Contributors ✨

Thank you to all of the wonderful people that have made this project possible. Non-code contributors are also much appreciated, and are listed here. Thank you to

• @francespoblete for much of Mitiq's design work/vision

Contributions of any kind are welcome!