Error mitigation for short-depth quantum circuits

TL;DR

This paper introduces two practical error mitigation schemes for short-depth quantum circuits, aiming to improve the accuracy of expectation value estimates in noisy intermediate-scale quantum devices.

Contribution

It presents two simple, resource-efficient error mitigation techniques—extrapolation and resampling—that do not require additional qubits and are suitable for current quantum experiments.

Findings

Extrapolation method effectively reduces noise in quantum expectation values.

Resampling with quasi-probability distributions cancels errors without extra qubits.

Both methods are practical for near-term quantum applications.

Abstract

Two schemes are presented that mitigate the effect of errors and decoherence in short depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation are introduced. Near-term applications of early quantum devices, such as quantum simulations, rely on accurate estimates of expectation values to become relevant. Decoherence and gate errors lead to wrong estimates of the expectation values of observables used to evaluate the noisy circuit. The two schemes we discuss are deliberately simple and don't require additional qubit resources, so to be as practically relevant in current experiments as possible. The first method, extrapolation to the zero noise limit, subsequently cancels powers of the noise perturbations by an application of Richardson's deferred approach to the limit. The second method cancels errors by resampling randomized circuits according to a quasi-probability distribution.