Discrete Abelian Gauge Theories for Quantum Simulations of QED

TL;DR

This paper explores a lattice gauge theory with discrete gauge symmetry to simulate quantum electrodynamics (QED) in one dimension, analyzing the effects of finite gauge fields and proposing an implementation strategy.

Contribution

It introduces a $ ext{Z}_n$ gauge model as an approximation to $U(1)$ QED for quantum simulation, including analysis of physical states and a potential implementation approach.

Findings

Finite gauge fields influence physical state properties.

The $ ext{Z}_n$ model approximates $U(1)$ for large n.

Proposes an effective dynamics method for simulation.

Abstract

We study a lattice gauge theory in Wilson's Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry $\mathbb{Z}_n$, approximating the $U(1)$ theory for large $n$. We analyze the role of the finiteness of the gauge fields and the properties of physical states, that satisfy a generalized Gauss's law. We finally discuss a possible implementation strategy, that involves an effective dynamics in physical space.