Filter Functions for Quantum Processes under Correlated Noise

TL;DR

This paper introduces a generalized filter function formalism to analyze quantum processes affected by correlated classical noise, enabling better understanding and quantification of noise effects on quantum gate sequences.

Contribution

It develops a perturbative method to compute quantum processes with correlated noise and derives a composition rule for filter functions of gate sequences.

Findings

Allows analysis of correlated noise effects on quantum gates

Enables quantitative studies of gate fidelities under correlated noise

Provides a tool for improved quantum noise characterization

Abstract

Many qubit implementations are afflicted by correlated noise not captured by standard theoretical tools that are based on Markov approximations. While independent gate operations are a key concept for quantum computing, it is actually not possible to fully describe noisy gates locally in time if noise is correlated on times longer than their duration. To address this issue, we develop a method based on the filter function formalism to perturbatively compute quantum processes in the presence of correlated classical noise. We derive a composition rule for the filter function of a sequence of gates in terms of those of the individual gates. The joint filter function allows to efficiently compute the quantum process of the whole sequence. Moreover, we show that correlation terms arise which capture the effects of the concatenation and thus yield insight into the effect of noise correlations on gate sequences. Our generalization of the filter function formalism enables both qualitative and quantitative studies of algorithms and state-of-the-art tools widely used for the experimental verification of gate fidelities like randomized benchmarking, even in the presence of noise correlations.