Colloquium

Simulating lattice gauge theories within quantum technologies

¹ Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
² Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Muenchen, Germany
³ Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21a, 6020 Innsbruck, Austria
⁴ Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
⁵ LENS and Dip. di Fisica e Astronomia, Università di Firenze, I-50019 Sesto Fiorentino, Italy
⁶ CNR-INO, S.S. Sesto Fiorentino, I-50019 Sesto Fiorentino, Italy
⁷ INFN Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy
⁸ Departament de Fisica, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Spain
⁹ SISSA, Via Bonomea 265, I-34136 Trieste, Italy
¹⁰ Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
¹¹ NIC, DESY, Platanenallee 6, D-15738 Zeuthen, Germany
¹² ICFO – Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
¹³ ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
¹⁴ Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova, I-35131 Padova, Italy
¹⁵ INFN Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy
¹⁶ School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel-Aviv 69978, Israel
¹⁷ Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
¹⁸ IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain
¹⁹ Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
²⁰ Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium
²¹ Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngaße 5, 1090 Vienna, Austria
²² Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstraße 5, CH-3012 Bern, Switzerland
²³ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
²⁴ Institute of Theoretical Physics, Jagiellonian University in Krakow, Lojasiewicza 11, 30-348 Kraków, Poland
²⁵ Mark Kac Complex Systems Research Center, Jagiellonian University, Lojasiewicza 11, 30-348 Kraków, Poland

^a e-mail: simone.montangero@unipd.it

Received: 11 November 2019
Received in final form: 26 May 2020
Published online: 4 August 2020

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.