Strategies for the Determination of the Running Coupling of $(2+1)$-dimensional QED with Quantum Computing

TL;DR

This paper explores using NISQ quantum devices to compute the mass gap in (2+1)-dimensional QED, aiming to determine the running coupling by combining quantum results with classical simulations and perturbation theory, as a step towards QCD studies.

Contribution

It introduces a quantum computing setup for (2+1)D QED, demonstrating mass gap calculations and proposing methods to determine the running coupling, bridging quantum and classical approaches.

Findings

Mass gap computed reliably in small and intermediate regimes.

Quantum results can be matched with Monte Carlo simulations.

Discussion of methods for computing the running coupling.

Abstract

We propose to utilize NISQ-era quantum devices to compute short distance quantities in $(2+1)$-dimensional QED and to combine them with large volume Monte Carlo simulations and perturbation theory. On the quantum computing side, we perform a calculation of the mass gap in the small and intermediate regime, demonstrating, in the latter case, that it can be resolved reliably. The so obtained mass gap can be used to match corresponding results from Monte Carlo simulations, which can be used eventually to set the physical scale. In this paper we provide the setup for the quantum computation and show results for the mass gap and the plaquette expectation value. In addition, we discuss some ideas that can be applied to the computation of the running coupling. Since the theory is asymptotically free, it would serve as a training ground for future studies of QCD in $(3+1)$-dimensions on quantum computers.