Z3 gauge theory coupled to fermions and quantum computing

TL;DR

This paper demonstrates the simulation of Z3 gauge theory coupled with fermions on a quantum computer using VQE, achieving accurate ground state energies and finite density EOS calculations, and discusses potential quantum advantage.

Contribution

It introduces a quantum computing approach to simulate Z3 gauge theory with fermions, including finite density effects, using VQE on IBM QISKit.

Findings

Accurate ground state energies obtained with up to 9 qubits.

Finite density EOS determined on quantum hardware.

Discussion of quantum advantage over classical methods.

Abstract

We study the Z3 gauge theory with fermions on the quantum computer using the Variational Quantum Eigensolver (VQE) algorithm with IBM QISKit software. Using up to 9 qubits we are able to obtain accurate results for the ground state energy. Introducing nonzero chemical potential we are able to determine the Equation of State (EOS) for finite density on the quantum computer. We discuss possible realizations of quantum advantage for this system over classical computers with regards to finite density simulations and the fermion sign problem.