Bounding the systematic error in quantum error mitigation due to model violation

TL;DR

This paper introduces a method to efficiently estimate the impact of inaccuracies in error models on quantum error mitigation, using no extra experiments and validated on real quantum hardware and simulations.

Contribution

It develops a novel protocol to bound the effects of error-model violations in quantum error mitigation, enabling better assessment of model quality without additional experiments.

Findings

Upper bounds are close to worst-case mitigation performance.

Method works on real IBM quantum hardware and simulations.

Observable error in deep circuits is not always maximized by Clifford circuits.

Abstract

Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens the question to what extent inaccuracy in the error model impacts the performance of error mitigation. In this work, we develop a methodology to efficiently compute upper bounds on the impact of error-model inaccuracy in error mitigation. Our protocols require no additional experiments, and instead rely on comparisons between the error model and the error-learning data from which the model is generated. We demonstrate the efficacy of our methodology by deploying it on an IBM Quantum superconducting qubit quantum processor, and through numerical simulation of standard error models. We show that our estimated upper bounds are typically close to the worst observed performance of error mitigation on random circuits. Our methodology can also be understood as an operationally meaningful metric to assess the quality of error models, and we further extend our methodology to allow for comparison between error models. Finally, contrary to what one might expect we show that observable error in noisy layered circuits of sufficient depth is not always maximized by a Clifford circuit, which may be of independent interest.