Gate fidelity fluctuations and quantum process invariants

TL;DR

This paper provides a detailed characterization of quantum gate fidelity fluctuations, deriving explicit formulas for variance and higher moments, with implications for quantum chaos and benchmarking.

Contribution

It introduces a state-independent method to compute the variance and higher moments of quantum gate fidelity, extending understanding of fidelity fluctuations.

Findings

Explicit expression for the variance of gate fidelity.

Asymptotic behavior of fidelity fluctuations in large systems.

Applications to quantum chaos and randomized benchmarking.

Abstract

We characterize the quantum gate fidelity in a state-independent manner by giving an explicit expression for its variance. The method we provide can be extended to calculate all higher order moments of the gate fidelity. Using these results we obtain a simple expression for the variance of a single qubit system and deduce the asymptotic behavior for large-dimensional quantum systems. Applications of these results to quantum chaos and randomized benchmarking are discussed.