Simulating Lattice Gauge Theories within Quantum Technologies

TL;DR

This paper reviews recent advances in simulating lattice gauge theories using quantum technologies, including classical tensor network methods and experimental implementations on various quantum hardware platforms.

Contribution

It introduces new tensor network simulation techniques and discusses experimental proposals and initial demonstrations for quantum simulation of lattice gauge theories.

Findings

Tensor network methods applied to Abelian and non-Abelian theories.

Proposals for implementing lattice gauge theories on trapped ions, Rydberg atoms, and superconducting circuits.

First proof-of-principle trapped ion experiments on the Schwinger model.

Abstract

Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach - applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.