A Practical Framework for Quantum Error Mitigation

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. The fraction of error-mitigated state that is successfully extracted, called extraction rate, will indicate the cost-effectiveness of the given mitigation scheme. Using the framework, we can derive and compare the fidelity boost, sampling overhead and extraction rate across various mitigation schemes under practical assumptions. The structure, insights and intuitions provided by the framework can serve as a basis for further developments of new schemes