Towards determining the (2+1)-dimensional Quantum Electrodynamics running coupling with Monte Carlo and quantum computing methods

TL;DR

This paper proposes a combined Monte Carlo and quantum computing approach to study the running coupling in (2+1)-dimensional lattice gauge theories, aiming to bridge perturbative and non-perturbative regimes.

Contribution

It introduces a novel methodology integrating quantum circuits with Monte Carlo simulations to determine the non-perturbative $\Lambda$-parameter in lattice gauge theories.

Findings

Quantum circuits can accurately capture gauge physics via plaquette expectation values.

The combined approach successfully relates static potential and force to the renormalized coupling.

Methodology can be extended to non-Abelian gauge theories with matter fields.

Abstract

In this paper, we examine a compact $U(1)$ lattice gauge theory in $(2+1)$ dimensions and present a strategy for studying the running coupling and extracting the non-perturbative $\Lambda$-parameter. To this end, we combine Monte Carlo simulations and quantum computing, where the former can be used to determine the numerical value of the lattice spacing $a$, and the latter allows for reaching the perturbative regime at very small values of the bare coupling and, correspondingly, small values of $a$. The methodology involves a series of sequential steps (i.e., the step scaling function) to bridge results from small lattice spacings to non-perturbative large-scale lattice calculations. Focusing on the pure gauge case, we demonstrate that these quantum circuits, adapted to gauge degrees of freedom, are able to capture the relevant physics by studying the expectation value of the plaquette operator, for matching with corresponding Monte Carlo simulations. We also present results for the static potential and static force, which can be related to the renormalized coupling. The procedure outlined in this work can be extended to Abelian and non-Abelian lattice gauge theories with matter fields and might provide a way towards studying lattice quantum chromodynamics utilizing both quantum and classical methods.