Error-mitigation aware benchmarking strategy for quantum optimization problems

TL;DR

This paper develops a benchmarking framework that incorporates finite-shot effects and quantum error mitigation to assess potential quantum advantage in noisy quantum optimization, demonstrated on the Fermi-Hubbard model.

Contribution

It introduces a new benchmarking approach that explicitly accounts for finite-shot statistics and QEM overhead, improving the assessment of quantum advantage in near-term devices.

Findings

Framework identifies regimes where PEC is advantageous.

Finite-shot effects do not hinder potential quantum advantage.

Provides a lightweight numerical tool for practical quantum advantage assessment.

Abstract

Assessing whether a noisy quantum device can potentially exhibit quantum advantage is essential for selecting practical quantum utility tasks that are not efficiently verifiable by classical means. For optimization, a prominent candidate for quantum advantage, entropy benchmarking provides insights based concomitantly on the specifics of the application and its implementation, as well as hardware noise. However, such an approach still does not account for finite-shot effects or for quantum error mitigation (QEM), a key near-term error suppression strategy that reduces estimation bias at the cost of increased sampling overhead. We address this limitation by developing a benchmarking framework that explicitly incorporates finite-shot statistics and the resource overhead induced by QEM. Our framework quantifies quantum advantage through the confidence that an estimated energy lies within an interval defined by the best-known classical upper and lower bounds. Using a proof-of-principle numerical study of the two-dimensional Fermi-Hubbard model at size $8\times8$, we demonstrate that the framework effectively identifies noise and shot-budget regimes in which the probabilistic error cancellation (PEC), a representative QEM method, is operationally advantageous, and potential quantum advantage is not hindered by finite-shot effects. Overall, our approach equips end-users with a framework based on lightweight numerics for assessing potential practical quantum advantage in optimization on near-future quantum hardware, in light of the allocated shot budget.