Bounding experimental quantum error rates relative to fault-tolerant thresholds

TL;DR

This paper develops tighter bounds on quantum error rates by incorporating unitarity and nonunital noise contributions, improving the assessment of fault-tolerance thresholds in quantum computing experiments.

Contribution

It introduces an improved method for bounding worst-case quantum errors using unitarity and analyzes the impact of nonunital noise, advancing fault-tolerance verification.

Findings

Bound on worst-case error can be improved using unitarity.

Nonunital noise contribution is negligible compared to coherent noise.

Average error rate scales similarly to worst-case error under certain measurement conditions.

Abstract

Rigorously establishing that the error in an experimental quantum operation is beneath the threshold for fault-tolerant quantum computation currently requires considering the worst-case error, which can be orders of magnitude smaller than the average gate infidelities routinely reported in experiments. We show that an improved bound on the worst-case error can be obtained by also considering the recently-introduced unitarity of the noise where the upper and lower bounds differ by a factor of $\approx 2.45$ for unital qubit channels. We prove that the contribution from the nonunital part of any noise map is at most on the order of the average gate infidelity and so is negligible relative to any coherent contribution. We also show that the "average" error rate when measurements are not restricted to an eigenbasis containing the state of the system exhibits the same scaling as the worst-case error, which, for coherent noise, is the square-root of the infidelity. We also obtain improved bounds for the diamond distance when the noise map is known (or approximately known).