Optimization of Richardson extrapolation for quantum error mitigation

TL;DR

This paper enhances quantum error mitigation by optimizing Richardson extrapolation, introducing a protocol for better noise reduction control and a novel set of nodes that outperform traditional choices without extra resources.

Contribution

It provides an in-depth analysis of Richardson extrapolation parameters, proposes an optimized implementation protocol, and introduces a new set of nodes that improve mitigation performance.

Findings

Optimized Richardson extrapolation protocol improves noise mitigation.

New set of nodes outperforms traditional nodes on average.

Enhanced control over statistical uncertainty in error mitigation.

Abstract

Quantum error mitigation is a key concept for the development of practical applications based on current noisy intermediate scale quantum (NISQ) devices. One of the most promising methods is Richardson extrapolation to the zero noise limit. While its main idea is rather simple, the full potential of Richardson extrapolation has not been completely uncovered yet. We give an in-depth analysis of the relevant parameters of Richardson extrapolation and propose an optimized protocol for its implementation. This protocol allows for a precise control of the increase in statistical uncertainty and lays the foundation for a significant improvement of the mitigation performance achieved by increasing the number of nodes. Furthermore, we present a novel set of nodes that, on average, outperforms the linear, exponential or Chebyshev nodes frequently used for Richardson extrapolation without requiring any additional resources.