Dihedral Lattice Gauge Theories on a Quantum Annealer

TL;DR

This paper explores implementing dihedral lattice gauge theories with non-Abelian discrete groups on a quantum annealer, demonstrating proof-of-principle calculations for ground states and time evolution.

Contribution

It extends the formalism of quantum annealer-based lattice gauge theory to finite non-Abelian groups, specifically dihedral groups, with practical demonstrations.

Findings

Successful proof-of-principle calculations of ground states.

Implementation of time evolution formalism with Feynman clock states.

Extension of quantum annealer methods to non-Abelian gauge groups.

Abstract

We study lattice gauge theory with discrete, non-Abelian gauge groups. We extend the formalism of previous studies on D-Wave's quantum annealer as a computing platform to finite, simply reducible gauge groups. As an example, we use the dihedral group $D_n$ with $n=3,4$ on a two plaquette ladder for which we provide proof-of-principle calculations of the ground-state and employ the known time evolution formalism with Feynman clock states.