Simulating $\mathbb{Z}_2$ lattice gauge theory on a quantum computer

TL;DR

This paper demonstrates quantum simulations of 1+1d $ ext{Z}_2$ gauge theory with matter, showing how error mitigation techniques significantly improve the accuracy of correlation functions and mass extraction on noisy quantum hardware.

Contribution

The study systematically evaluates multiple quantum error mitigation strategies in simulating lattice gauge theories, highlighting their combined effectiveness in extending reliable simulation times.

Findings

Error mitigation extends accurate correlation function calculations by a factor of six.

Quantum simulations successfully extract the mass of the lightest spin-1 state.

Error mitigation is crucial for reliable quantum gauge theory simulations.

Abstract

The utility of quantum computers for simulating lattice gauge theories is currently limited by the noisiness of the physical hardware. Various quantum error mitigation strategies exist to reduce the statistical and systematic uncertainties in quantum simulations via improved algorithms and analysis strategies. We perform quantum simulations of $1+1d$ $\mathbb{Z}_2$ gauge theory with matter to study the efficacy and interplay of different error mitigation methods: readout error mitigation, randomized compiling, rescaling, and dynamical decoupling. We compute Minkowski correlation functions in this confining gauge theory and extract the mass of the lightest spin-1 state from fits to their time dependence. Quantum error mitigation extends the range of times over which our correlation function calculations are accurate by a factor of six and is therefore essential for obtaining reliable masses.