Characterizing the ultimate potential and limitations of quantum error mitigation

The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Although numerous quantum error-mitigation protocols have been proposed, their general potential and limitations have still been elusive, hindering us from pinpointing the theoretical goal that new error-mitigation proposals should aim at. In this talk, I will review recent advances in the general theory of quantum error mitigation toward characterizing its ultimate capability. I will introduce universal performance bounds applicable to general error-mitigation protocols, which provide an effective platform to discuss the optimality of specific mitigation methods among a general class. I will apply these bounds to show that the number of samples required for general mitigation protocols must grow exponentially with the circuit depth for various noise models, revealing the fundamental obstacles in showing useful applications of noisy near-term quantum devices.

This talk includes results reported in R. Takagi, S. Endo, S. Minagawa, M. Gu, "Fundamental limits of quantum error mitigation", npj Quantum Inf. 8, 114 (2022), and R. Takagi, H. Tajima, M. Gu, "Universal sample lower bounds for quantum error mitigation", arXiv:2208.09178.