Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise

TL;DR

This paper develops a comprehensive theoretical framework for randomized benchmarking that accounts for non-Markovian, temporally-correlated noise, enabling more accurate characterization of quantum gate fidelities in complex, realistic quantum systems.

Contribution

It introduces a general expression for Average Sequence Fidelity under non-Markovian noise and establishes conditions to detect genuine non-Markovian effects in quantum benchmarking.

Findings

Derived a general ASF expression for non-Markovian noise

Proposed methods to measure average gate fidelities with non-Markovian processes

Showed ASF stability under small gate-dependent perturbations

Abstract

The rapid progress in the development of quantum devices is in large part due to the availability of a wide range of characterization techniques allowing to probe, test and adjust them. Nevertheless, these methods often make use of approximations that hold in rather simplistic circumstances. In particular, assuming that error mechanisms stay constant in time and have no dependence in the past, is something that will be impossible to do as quantum processors continue scaling up in depth and size. We establish a theoretical framework for the Randomized Benchmarking protocol encompassing temporally-correlated, so-called non-Markovian noise, at the gate level, for any gate set belonging to a wide class of finite groups. We obtain a general expression for the Average Sequence Fidelity (ASF) and propose a way to obtain average gate fidelities of full non-Markovian noise processes. Moreover, we obtain conditions that are fulfilled when an ASF displays authentic non-Markovian deviations. Finally, we show that even though gate-dependence does not translate into a perturbative term within the ASF, as in the Markovian case, the non-Markovian sequence fidelity nevertheless remains stable under small gate-dependent perturbations.