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

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
Robust Shadow Estimation 🚧	RSE	mitiq.qse	2011.09636 2002.08953
Layerwise Richardson Extrapolation	LRE	mitiq.lre	2402.04000
Probabilistic Error Amplification 🚧	Coming soon	mitiq.pea	Nature

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:

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!