<a href="https://github.com/unitaryfoundation/mitiq"><img src="https://raw.githubusercontent.com/unitaryfoundation/mitiq/main/docs/source/img/mitiq-logo.png" alt="Mitiq logo" width="350"/></a>

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)

Mitiq

Install / Use

README