Characterizing noisy quantum computation with imperfectly addressed errors

TL;DR

This paper develops a new theoretical framework using random matrix theory to analyze how realistic noise impacts quantum computation, helping to diagnose when quantum outputs can be trusted.

Contribution

It introduces a novel approach to characterize noise effects in quantum computing via spectral analysis of random superoperators, addressing limitations of previous simulation methods.

Findings

Spectral distributions depend on noise violations of protocol assumptions

Framework enables analysis of spectral gaps and relaxation times

Provides tools for diagnosing trustworthiness of noisy quantum outputs

Abstract

Quantum protocols on hardware are subject to noise that prohibits performance. Protocols for addressing errors, such as error correction or error mitigation, may fail to combat errors in quantum computation if noise violates critical assumptions required for these protocols to be effective. However, tools for characterizing such failures in realistic operating conditions are limited. For example, while brute force simulations may be used to characterize the impact of such failures on a handful of input states, such simulations lack a complete description for how noise transforms state-spaces in the full quantum Hilbert space. In this work, we associate quantum computation subject to realistic noise to an ensemble of random superoperators and study the eigen- and singular spectral distributions over this ensemble. We propose a new theoretical framework to characterize singular values of random complex matrices using matrix Chernoff concentration. Using our framework, we analyze imperfectly addressed errors in error mitigation and error correction. We find that distributions of singular spectra depend on how noise violates critical assumptions of these protocols. Finally, we quantitatively discuss how our work may be applied to understanding limiting behavior of quantum computation, such as establishing spectral gaps and relaxation times for specific families of quantum Markov processes. Our work paves the way for new tools to diagnose when to trust the output of noisy quantum computers.