Digital quantum simulation of lattice gauge theories in three spatial dimensions

TL;DR

This paper presents a digital quantum simulation scheme for 3+1 dimensional lattice gauge theories with dynamical fermions, enabling stronger interactions without perturbation theory and applicable to various gauge groups.

Contribution

It introduces a novel stroboscopic sequence-based digital simulation method for lattice gauge theories in three spatial dimensions, including non-Abelian groups, using ultracold atoms.

Findings

Simulation scheme avoids perturbation theory for magnetic interactions

Applicable to compact and finite gauge groups

Proposed implementation with ultracold atoms in optical lattices

Abstract

In the present work, we propose a scheme for digital formulation of lattice gauge theories with dynamical fermions in 3+1 dimensions. All interactions are obtained as a stroboscopic sequence of two-body interactions with an auxiliary system. This enables quantum simulations of lattice gauge theories where the magnetic four-body interactions arising in two and more spatial dimensions are obtained without the use of perturbation theory, thus resulting in stronger interactions compared with analogue approaches. The simulation scheme is applicable to lattice gauge theories with either compact or finite gauge groups. The required bounds on the digitization errors in lattice gauge theories, due to the sequential nature of the stroboscopic time evolution, are provided. Furthermore, an implementation of a lattice gauge theory with a non-abelian gauge group, the dihedral group $D_{3}$, is proposed employing the aforementioned simulation scheme using ultracold atoms in optical lattices.