Investigating the limits of randomized benchmarking protocols

TL;DR

This paper evaluates the effectiveness of randomized benchmarking protocols across various realistic error models, demonstrating their reliability in estimating quantum gate errors and deriving new fidelity decay models for non-Markovian noise.

Contribution

It provides a comprehensive analysis of randomized benchmarking performance under complex error conditions and introduces new models for fidelity decay with non-Markovian noise.

Findings

Benchmarking estimates are within a factor of two of true error rates.

Few trials are needed for high-confidence error estimation.

New fidelity decay models for non-Markovian noise are derived.

Abstract

In this paper, we analyze the performance of randomized benchmarking protocols on gate sets under a variety of realistic error models that include systematic rotations, amplitude damping, leakage to higher levels, and 1/f noise. We find that, in almost all cases, benchmarking provides better than a factor-of-two estimate of average error rate, suggesting that randomized benchmarking protocols are a valuable tool for verification and validation of quantum operations. In addition, we derive new models for fidelity decay curves under certain types of non-Markovian noise models such as 1/f and leakage errors. We also show that, provided the standard error of the fidelity measurements is small, only a small number of trials are required for high confidence estimation of gate errors.