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.
• For code, repo, or theory questions, especially those requiring more detailed responses, submit a Discussion.
• For casual or time sensitive questions, chat with mitiq developers on the #mitiq channel on Discord.
• Contributions to Mitiq are eligible for compensation! More details here, and all payouts can be found on our wiki!

Quickstart

Installation

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.

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 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

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
Layerwise Richardson Extrapolation	LRE	mitiq.lre	2402.04000

The following techniques are experimental and must be imported via from mitiq import experimental. Experimental techniques are not covered by mitiq's semantic versioning guarantees. A technique graduates to stable once it has broad test coverage, documented user guides, and has seen real-world validation on hardware or well-studied noise models. If you are using an experimental technique and would like to help it graduate, please open an issue or contribute to the discussion on GitHub.

Technique	Documentation	Mitiq module	Paper Reference(s)
Robust Shadow Estimation	RSE	mitiq.experimental.shadows	2011.09636 2002.08953
Probabilistic Error Amplification	PEA	mitiq.experimental.pea	Nature
Virtual Distillation	VD	mitiq.experimental.vd	APS
Twirled Readout Error eXtinction	TREX	mitiq.experimental.trex	2012.09738

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	mitiq.pt	1512.01098

If there is a technique you are looking for not listed here, please file a feature request.

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	Qiskit	pyQuil	Braket	PennyLane	Qibo	OpenQASM 3

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:

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.

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.

Contributions of all kinds are welcome! We accept AI-assissted contributions, and we ask contributors to be transparent about how they are using AI tooling to help reviewers best review contributions. See the contributing documentation for more details on the policy.

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