Randomized benchmarking in the presence of time-correlated dephasing noise

TL;DR

This paper investigates how time-correlated dephasing noise affects the exponential decay assumption in randomized benchmarking, providing insights into deviations caused by noise correlations in quantum gate fidelity measurements.

Contribution

It offers an exact analysis of randomized benchmarking under time-correlated dephasing noise, clarifying when deviations from exponential decay occur.

Findings

Deviations from exponential decay are linked to specific noise correlation structures.

Exact solutions reveal conditions under which standard benchmarking assumptions break down.

Insights help improve interpretation of benchmarking results in realistic noisy environments.

Abstract

Randomized benchmarking has emerged as a popular and easy-to-implement experimental technique for gauging the quality of gate operations in quantum computing devices. A typical randomized benchmarking procedure identifies the exponential decay in the fidelity as the benchmarking sequence of gates increases in length, and the decay rate is used to estimate the fidelity of the gate. That the fidelity decays exponentially, however, relies on the assumption of time-independent or static noise in the gates, with no correlations or significant drift in the noise over the gate sequence, a well-satisfied condition in many situations. Deviations from the standard exponential decay, however, have been observed, usually attributed to some amount of time correlations in the noise, though the precise mechanisms for deviation have yet to be fully explored. In this work, we examine this question of randomized benchmarking for time-correlated noise---specifically for time-correlated dephasing noise for exact solvability---and elucidate the circumstances in which a deviation from exponential decay can be expected.