  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.
