Toward Exploring Phase Diagrams of Gauge Theories on Quantum Computers with Thermal Pure Quantum States

TL;DR

This paper proposes a quantum computing approach using thermal pure quantum states to simulate finite-temperature gauge theories at non-zero density, aiming to overcome classical sign problems in lattice QCD.

Contribution

It introduces a sign-problem-free quantum method for thermal calculations in lattice gauge theories, extending the thermal pure-quantum-state formalism to gauge systems.

Findings

Demonstrates feasibility on a simple $ ext{Z}_2$ lattice gauge theory

Analyzes resource requirements for near-term quantum hardware

Shows robustness to algorithmic and hardware imperfections

Abstract

Aiming at evading the notorious sign problem in classical Monte-Carlo approaches to lattice quantum chromodynamics, we present an approach for quantum computing finite-temperature lattice gauge theories at non-zero density. Based on the thermal pure-quantum-state formalism of statistical mechanics when extended to gauge-theory systems, our approach allows for sign-problem-free quantum computations of thermal expectation values and non-equal time correlation functions. By taking a simple lattice gauge theory for which classical benchmarks are possible, namely $\mathbb{Z}_2$ lattice gauge theory in 1+1 dimensions at finite chemical potential, we discuss resource requirements and robustness to algorithmic and hardware imperfections for near-term quantum-hardware realizations.