Quantum simulation of lattice gauge theories using Wilson fermions

TL;DR

This paper explores how optimizing the discretization of the Dirac Hamiltonian using Wilson fermions can enhance quantum simulation of lattice gauge theories, demonstrated with a proposed ultracold atom experiment for simulating the Schwinger mechanism.

Contribution

It introduces an optimized lattice formulation with Wilson fermions for quantum simulation of gauge theories, simplifying experimental setups and reducing resource requirements.

Findings

Wilson fermions enable simpler optical lattice setups.

Reduced degrees of freedom for dynamical gauge fields.

Quantum simulator can access the Schwinger mechanism.

Abstract

Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum simulation of lattice gauge theories, however, hinges crucially on the efficient use of experimental resources. As we argue in this work, due to the fundamental non-uniqueness of discretizing the relativistic Dirac Hamiltonian, the lattice representation of gauge theories allows for an optimization that up to now has been left unexplored. We exemplify our discussion with lattice quantum electrodynamics in two-dimensional space-time, where we show that the formulation through Wilson fermions provides several advantages over the previously considered staggered fermions. Notably, it enables a strongly simplified optical lattice setup and it reduces the number of degrees of freedom required to simulate dynamical gauge fields. Exploiting the optimal representation, we propose an experiment based on a mixture of ultracold atoms trapped in a tilted optical lattice. Using numerical benchmark simulations, we demonstrate that a state-of-the-art quantum simulator may access the Schwinger mechanism and map out its non-perturbative onset.