Quantum sampling for the Euclidean path integral of lattice gauge theory

TL;DR

This paper explores using quantum sampling algorithms to generate gauge configurations in lattice gauge theory within the path integral formalism, demonstrating benefits like Lorentz invariance and leveraging classical simulation knowledge.

Contribution

It introduces a quantum sampling approach for lattice gauge theory in the path integral formalism, providing a benchmark test on $Z_2$ gauge theory.

Findings

Successful benchmark on $Z_2$ lattice gauge theory

Demonstrates feasibility of quantum sampling in path integral formalism

Highlights advantages over Hamiltonian formalism

Abstract

Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience accumulated by classical lattice simulation and manifest Lorentz invariance. We discuss quantum computation of lattice gauge theory in the path integral formalism. We utilize a quantum sampling algorithm to generate gauge configurations, and demonstrate a benchmark test of $Z_2$ lattice gauge theory on a four-dimensional hypercube.