Randomized Benchmarking with Confidence

TL;DR

This paper proves that randomized benchmarking provides highly precise estimates of quantum gate errors with rigorous confidence bounds, even for time-dependent Markovian noise, and offers methods to detect non-Markovian noise.

Contribution

It establishes the statistical reliability of randomized benchmarking for various noise types and guides experimental parameter choices for accurate quantum noise characterization.

Findings

Randomized benchmarking estimates are highly precise with small variance.

The method provides rigorous confidence bounds for average gate errors.

It can reliably characterize time-dependent Markovian noise and detect non-Markovianity.

Abstract

Randomized benchmarking is a promising tool for characterizing the noise in experimental implementations of quantum systems. In this paper, we prove that the estimates produced by randomized benchmarking (both standard and interleaved) for arbitrary Markovian noise sources are remarkably precise by showing that the variance due to sampling random gate sequences is small. We discuss how to choose experimental parameters, in particular the number and lengths of random sequences, in order to characterize average gate errors with rigorous confidence bounds. We also show that randomized benchmarking can be used to reliably characterize time-dependent Markovian noise (e.g., when noise is due to a magnetic field with fluctuating strength). Moreover, we identify a necessary property for time-dependent noise that is violated by some sources of non-Markovian noise, which provides a test for non-Markovianity.