Error Mitigation for Short-Depth Quantum Circuits

TLDR

The applicability of error‑mitigation schemes is limited by error rates, and near‑term quantum simulations depend on accurate expectation values, which decoherence and gate errors corrupt, so the presented schemes aim to be simple and resource‑efficient for current experiments. The paper presents two schemes to mitigate errors and decoherence in short‑depth quantum circuits. Both schemes are deliberately simple and require no extra qubits; the first uses Richardson extrapolation to cancel noise perturbations, and the second resamples randomized circuits according to a quasi‑probability distribution.

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.