$U(N)$ gauge theory in the strong coupling limit on a quantum annealer

TL;DR

This paper explores reformulating lattice gauge theories in the strong coupling regime as combinatorial optimization problems suitable for quantum annealers, demonstrating initial results on D-Wave for certain gauge groups and outlining future steps.

Contribution

It introduces a novel approach to simulate lattice gauge theories using quantum annealing by reformulating the problem as a combinatorial optimization task, enabling studies at low temperatures.

Findings

Initial results obtained on D-Wave for U(1) and U(3) gauge groups.

Histogram reweighting improves observable accuracy.

Outlines future steps for simulating SU(3) gauge group.

Abstract

Lattice QCD in the strong coupling regime can be formulated in dual variables which are integer-valued. It can be efficiently simulated for modest finite temperatures and finite densities via the worm algorithm, circumventing the finite density sign problem in this regime. However, the low temperature regime is more expensive to address. As the partition function is solely expressed in terms of integers, it can be cast as a combinatorial optimization problem that can be solved on a quantum annealer. We will first explain the setup of the system we want to study, and then present its reformulation suitable for a quantum annealer, and in particular the D-Wave. As a proof of concept, we present first results obtained on D-Wave for gauge group $U(1)$ and $U(3)$, and outline the next steps towards gauge groups $SU(3)$. We find that in addition, histogram reweighting greatly improves the accuracy of our observables when compared to analytic results.