Quantum anomaly for benchmarking quantum computing

TL;DR

This paper proposes using the axial anomaly in gauge theories as a benchmark for quantum simulations, demonstrating its feasibility on current quantum computers to verify quantum computations.

Contribution

It introduces the axial anomaly as a novel, exact benchmark for quantum simulation verification in lattice gauge theories, validated through experiments on a trapped-ion quantum computer.

Findings

Successfully simulated axial-charge production in ${ m Z}_N$ lattice gauge theories

Reproduced the anomaly coefficient within statistical uncertainties

Demonstrated the feasibility of using axial anomaly as a verification test for quantum computers

Abstract

Given the rapid advances in quantum computing hardware, establishing systematic strategies for verifying the correctness of quantum computations has become increasingly important. Exploiting the fact that the axial anomaly in gauge theories is exact to all orders in perturbation theory, we propose the axial anomaly as a nontrivial benchmark for quantum simulations of lattice gauge theories. We simulate anomalous axial-charge production in ${\mathbb Z}_N$ lattice gauge theories on the trapped-ion quantum computer ``Reimei''. After taking the U(1), infinitesimal time, and infinite volume limits, we successfully reproduce the anomaly coefficient within statistical uncertainties, even without error mitigation. Our results demonstrate that the axial anomaly can be simulated on current quantum computers and serves as a verification test of quantum computations.