Comparing Experiments to the Fault-Tolerance Threshold

TL;DR

This paper explores the relationship between average error rates measured in experiments and the worst-case error thresholds critical for fault-tolerance in quantum computing, highlighting the impact of coherent errors.

Contribution

It derives relations between average and worst-case error rates for various noise sources, clarifying how to compare experimental results with theoretical fault-tolerance thresholds.

Findings

Coherent errors cause large discrepancies between average and worst-case errors.

Quantifies how well coherent errors must be controlled for accurate threshold comparison.

Provides a framework for relating experimental error rates to fault-tolerance thresholds.

Abstract

Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between measured error rates and thresholds is complicated by the fact that benchmarking estimates average error rates while thresholds reflect worst-case behavior when a gate is used as part of a large computation. These two measures of error can differ by orders of magnitude in the regime of interest. Here we facilitate comparison between the experimentally accessible average error rates and the worst-case quantities that arise in current threshold theorems by deriving relations between the two for a variety of physical noise sources. Our results indicate that it is coherent errors that lead to an enormous mismatch between average and worst case, and we quantify how well these errors must be controlled to ensure fair comparison between average error probabilities and fault-tolerance thresholds.