Review on Quantum Computing for Lattice Field Theory

TL;DR

This review discusses recent progress in applying quantum computing to lattice field theory, highlighting potential advantages, current achievements, and future challenges in simulating complex quantum systems.

Contribution

It provides a comprehensive overview of recent quantum algorithms and proof-of-concept experiments for lattice gauge theories, emphasizing the path toward higher-dimensional simulations.

Findings

First quantum computations of lattice gauge theories in (1+1) dimensions.

Development of resource-efficient quantum algorithms for (1+1) and (2+1) dimensions.

Identification of challenges and future directions for (3+1)-dimensional lattice QCD simulations.

Abstract

In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimensions have been accomplished, and first resource-efficient quantum algorithms for lattice gauge theories in (1+1) and (2+1) dimensions have been developed. The path towards quantum computations of (3+1)-dimensional lattice gauge theories, including Lattice QCD, requires many incremental steps of improving both quantum hardware and quantum algorithms. After reviewing these requirements and recent advances, we discuss the main challenges and future directions.