Operational Markovianization in randomized benchmarking

Abstract

A crucial task to obtain optimal and reliable quantum devices is to quantify their overall performance. The average fidelity of quantum gates is a particular figure of merit that can be estimated efficiently by randomized benchmarking (RB). However, the concept of gate-fidelity itself relies on the crucial assumption that noise behaves in a predictable, time-local, or so-called Markovian manner, whose breakdown can naturally become the leading source of errors as quantum devices scale in size and depth. We analytically show that error suppression techniques such as dynamical decoupling (DD) and Pauli-twirling can operationally Markovianize RB: (i) fast DD reduces non-Markovian RB to an exponential decay plus longer-time corrections, while on the other hand, (ii) Pauli-twirling generally does not affect the average, but (iii) it always suppresses the variance of such RB outputs. We demonstrate these effects numerically with a qubit noise model. Our results show that simple and efficient error suppression methods can simultaneously tame non-Markovian noise and allow for standard and reliable gate quality estimation, a fundamentally important task in the path toward fully functional quantum devices.