Quantum circuit for $\mathbb{Z}_3$ lattice gauge theory at nonzero baryon density

TL;DR

This paper explores quantum simulation of $ ext{Z}_3$ lattice gauge theory at nonzero baryon density, demonstrating how to study baryonic matter's ground state properties using quantum emulators.

Contribution

It introduces a quantum simulation framework for $ ext{Z}_3$ lattice gauge theory, highlighting methods to analyze baryonic matter at finite density.

Findings

Quantum emulator calculations of the ground state of baryonic matter.

Demonstration of gauge symmetry importance in quantum simulations.

Feasibility of studying nonzero baryon density in discrete gauge theories.

Abstract

$\mathbb{Z}_3$ lattice gauge theory is the simplest discrete gauge theory with three-quark bound states, i.e., baryons. Since it has a finite-dimensional Hilbert space, it can be used for testing quantum simulation of lattice gauge theory at nonzero baryon density. We discuss global and local gauge symmetries and their importance in quantum simulation. We perform quantum emulator calculation and demonstrate how to study the ground state property of baryonic matter.