Randomized Benchmarking, Correlated Noise, and Ising Models

TL;DR

This paper links randomized benchmarking fidelity under correlated noise to Ising models, revealing how noise correlations affect fidelity decay and the reliability of error rate estimates.

Contribution

It introduces a novel connection between randomized benchmarking and Ising models, providing a new framework to analyze the effects of correlated noise on quantum gate fidelity.

Findings

Fidelity under correlated noise maps to Ising model partition functions.

Decay transitions from exponential to power law with noise correlation.

Exponential fits can misestimate gate error rates under correlated noise.

Abstract

We compute the expected randomized benchmarking sequence fidelity for a system subject to Gaussian time-correlated noise. For single qubit benchmarking we show that the expected sequence fidelity is given by the partition function of a long-range coupled spin-one Ising model, with each site in the Ising model corresponding to a free evolution interval. For d-state systems, the expected sequence fidelity is given by an Ising-like model partition function whose site variables are given by the weights of the adjoint representation of SU(d). A high effective temperature expansion for the partition function in the single qubit case shows decay of sequence fidelity varying from exponential for uncorrelated noise to a power law for quasistatic noise. Fitting an exponential to the sequence fidelity decay under correlated noise gives unreliable estimates of the average gate error rate.