A Practical Framework for Quantum Error Mitigation

TL;DR

This paper introduces a comprehensive framework called linear quantum error mitigation that unifies existing schemes, providing a basis for comparing their efficiency and guiding future development in practical quantum computing applications.

Contribution

It constructs a general framework for quantum error mitigation that includes most current schemes and introduces a new metric called extraction rate for evaluating their cost-effectiveness.

Findings

Derived and compared extraction rates across schemes

Analyzed fidelity improvements and sampling overheads

Provided insights for developing new mitigation strategies

Abstract

Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error mitigation schemes proposed under a coherent framework that can highlight their underlying connections while providing guidance for their practical performance. In this article, we construct a general framework named linear quantum error mitigation that includes most of the state-of-the-art quantum error mitigation schemes. Within the framework, quantum error mitigation can be effectively viewed as extracting the error-mitigated state out of the noisy state, which introduces a new metric called extraction rate for indicating the cost-effectiveness of a given mitigation scheme. Using the framework, we have derived and compared the extraction rate, improvement in the fidelity and sampling overhead across various mitigation schemes under practical assumptions. The structure, insights and intuitions provided by the framework can serve as a basis for the further development of new schemes.