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

Abstract

The solution of strongly-interacting quantum field theories remains a major challenge in theoretical physics, often requiring numerical solutions. A first-principles approach in this direction is the lattice formulation, where spacetime is approximated with a finite grid. In this work, we examine the case of a compact pure-gauge U(1) lattice gauge theory in (2 + 1) dimensions, presenting a strategy to determine the running coupling of the theory and extracting the non-perturbative Λ-parameter. This is achieved by combining Monte Carlo simulations and quantum computing techniques, matching the expectation value of the plaquette operator. We also present results for the static potential and static force, which can be related to the renormalized coupling. The outlined procedure can be extended to other 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.