The Accuracy vs. Sampling Overhead Trade-off in Quantum Error Mitigation Using Monte Carlo-Based Channel Inversion

TL;DR

This paper analyzes the trade-off between accuracy and sampling overhead in quantum error mitigation using Monte Carlo-based channel inversion, showing that QEM maintains favorable error scaling even with practical sampling strategies.

Contribution

It introduces a Monte Carlo sampling-based channel inversion method for QEM and analyzes its impact on error scaling and sampling overhead in practical scenarios.

Findings

QEM error scales with the square root of the number of gates when computational error is small.

Without QEM, error scales linearly with the number of gates.

QEM remains preferable in error scaling despite additional sampling overhead.

Abstract

Quantum error mitigation (QEM) is a class of promising techniques for reducing the computational error of variational quantum algorithms. In general, the computational error reduction comes at the cost of a sampling overhead due to the variance-boosting effect caused by the channel inversion operation, which ultimately limits the applicability of QEM. Existing sampling overhead analysis of QEM typically assumes exact channel inversion, which is unrealistic in practical scenarios. In this treatise, we consider a practical channel inversion strategy based on Monte Carlo sampling, which introduces additional computational error that in turn may be eliminated at the cost of an extra sampling overhead. In particular, we show that when the computational error is small compared to the dynamic range of the error-free results, it scales with the square root of the number of gates. By contrast, the error exhibits a linear scaling with the number of gates in the absence of QEM under the same assumptions. Hence, the error scaling of QEM remains to be preferable even without the extra sampling overhead. Our analytical results are accompanied by numerical examples.