# Statistical analysis of randomized benchmarking

## TL;DR

This paper improves randomized benchmarking for quantum computers by proposing a modification that enhances accuracy, simplifies experimental procedures, and provides reliable error estimates with credible regions.

## Contribution

It introduces a simple modification to RB+ that eliminates a nuisance parameter and improves the efficiency and reliability of error rate estimation.

## Key findings

- Eliminates a nuisance parameter in RB+
- Provides a method for credible regions of parameters
- Achieves error estimates with multiplicative precision

## Abstract

Randomized benchmarking and variants thereof, which we collectively call RB+, are widely used to characterize the performance of quantum computers because they are simple, scalable, and robust to state-preparation and measurement errors. However, experimental implementations of RB+ allocate resources suboptimally and make ad-hoc assumptions that undermine the reliability of the data analysis. In this paper, we propose a simple modification of RB+ which rigorously eliminates a nuisance parameter and simplifies the experimental design. We then show that, with this modification and specific experimental choices, RB+ efficiently provides estimates of error rates with multiplicative precision. Finally, we provide a simplified rigorous method for obtaining credible regions for parameters of interest and a heuristic approximation for these intervals that performs well in currently relevant regimes.