Randomized benchmarking with confidence

Joel J Wallman,Steven T Flammia

doi:10.1088/1367-2630/16/10/103032

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.

Highlights

It is possible to completely characterize an experimental implementation of a unitary using full quantum process tomography [2, 3]. This approach is impractical for large quantum systems since it involves an exponential amount of resources in the number of qubits and it is sensitive to state preparation and measurement (SPAM) errors, which create a noise floor below which an accurate process estimation becomes impossible [4]
A partial characterization of, for example, the average error rate and/or the worst-case error rate compared to a perfect implementation of a target unitary is typically enough to determine whether an experimental implementation of a unitary is sufficient for achieving fault-tolerance in a specific scheme for fault-tolerant quantum computation
While direct fidelity estimation gives an unconditional and assumption-free estimate of the average gate fidelity, it is prone to state preparation and measurement (SPAM) errors, which leads to conflation of noise sources

Summary

Introduction

The main result of this paper is to prove the first rigorous confidence interval on randomized benchmarking, the de facto standard method for characterizing the accuracy of experimental implementations of quantum gates. This approach is impractical for large quantum systems since it involves an exponential amount of resources in the number of qubits and it is sensitive to state preparation and measurement (SPAM) errors, which create a noise floor below which an accurate process estimation becomes impossible [4].

Results

Conclusion