Random matrix perspective on probabilistic error cancellation

TL;DR

This paper explores the spectral properties of unphysical channels used in probabilistic error cancellation in quantum computing, using random matrix theory to understand their structure and effects.

Contribution

It introduces a random matrix ensemble model for noisy quantum algorithms to analyze the properties of denoiser channels and their spectral characteristics.

Findings

Spectra of denoiser channels reflect random Lindbladian structures.

Local noise channels induce a hierarchy of timescales.

Random matrix models reveal insights into error mitigation techniques.

Abstract

Probabilistic error cancellation is an attempt to reverse the effect of dissipative noise channels on quantum computers by applying unphysical channels after the execution of a quantum algorithm on noisy hardware. We investigate on general grounds the properties of such unphysical quantum channels by considering a random matrix ensemble modeling noisy quantum algorithms. We show that the complex spectra of denoiser channels inherit their structure from random Lindbladians. Additional structure imposed by the locality of noise channels of the quantum computer emerges in terms of a hierarchy of timescales.