Simulating Lattice Gauge Theories Within Quantum Technologies
Total Page：16
File Type：pdf, Size：1020Kb
EPJ manuscript No. (will be inserted by the editor) Simulating Lattice Gauge Theories within Quantum Technologies M.C. Ba~nuls1;2, R. Blatt3;4, J. Catani5;6;7, A. Celi3;8, J.I. Cirac1;2, M. Dalmonte9;10, L. Fallani5;6;7, K. Jansen11, M. Lewenstein8;12;13, S. Montangero7;14 a, C.A. Muschik3, B. Reznik15, E. Rico16;17 b, L. Tagliacozzo18, K. Van Acoleyen19, F. Verstraete19;20, U.-J. Wiese21, M. Wingate22, J. Zakrzewski23;24, and P. Zoller3 1 Max-Planck-Institut f¨urQuantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany 2 Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Muenchen, Germany 3 Institut f¨urQuantenoptik und Quanteninformation, Osterreichische¨ Akademie der Wissenschaften, Technikerstraße 21a, 6020 Innsbruck, Austria 4 Institut f¨urExperimentalphysik, Universit¨atInnsbruck, Technikerstraße 25, 6020 Innsbruck, Austria 5 LENS and Dip. di Fisica e Astronomia, Universit`adi Firenze, 50019 Sesto Fiorentino, Italy 6 CNR-INO, S.S. Sesto Fiorentino, 50019 Sesto Fiorentino, Italy 7 INFN Istituto Nazionale di Fisica Nucleare, 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 Ci`encies Fot`oniques,The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain 13 ICREA, Pg. Llu´ısCompanys 23, 08010 Barcelona, Spain 14 Dipartimento di Fisica e Astronomia G. Galilei, Universit`adegli Studi di Padova, I-35131 Padova, Italy 15 School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel-Aviv 69978, Israel 16 Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain 17 IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain 18 Departament de F´ısicaQu`antica i Astrof´ısicaand Institut de Ci`enciesdel Cosmos (ICCUB), Universitat de Barcelona, Mart´ı i Franqu`es1, 08028 Barcelona, Spain 19 Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium 20 Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngaße 5, 1090 Vienna, Austria 21 Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstraße 5, CH- 3012 Bern, Switzerland 22 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK 23 Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagiellonski, Lojasiewicza 11, 30-348 Krakow, Poland 24 Mark Kac Complex Systems Research Center, Jagiellonian University, Lojasiewicza 11, 30-348 Krakow, Poland November 4, 2019 Abstract Lattice gauge theories, which originated from particle physics in the context of Quantum Chro- modynamics (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 arXiv:1911.00003v1 [quant-ph] 31 Oct 2019 information science. In this way, lattice gauge theories provide both motivation and a framework for inter- disciplinary 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 cir- cuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. PACS. XX.XX.XX No PACS code given 2 M.C. Ba~nulset al.: Simulating Lattice Gauge Theories within Quantum Technologies 1 Introduction munities to study strongly correlated many-body quantum systems[17]. Indeed, as it has been shown recently, TNM In the last few decades, quantum information theory has can be exploited to study LGT going in regimes where been fast developing and consequently its application to standard approaches are severely limited[18, 19]. the real world has spawned different technologies that { Lattice gauge theory was originally constructed by Wil- as for classical information theory { encompass the fields son in order to define Quantum Chromodynamics (QCD) of communication, computation, sensing, and simulation | the relativistic SU(3) gauge field theory that describes [1, 2, 3]. To date, the technological readiness level of quan- the strong interaction between quarks and gluons | be- tum technologies is highly diverse: some quantum commu- yond perturbation theory. For this purpose, he introduced nication protocols are ready for the market, while, e.g., a hyper-cubic space-time lattice as a gauge invariant regu- universal quantum computers { despite experiencing an lator of ultraviolet divergences, with quark fields residing incredibly fast development { are still at the first develop- on lattice sites and gluons fields residing on links connect- ment stage[4, 5]. ing nearest-neighbour sites. This framework makes nu- Some particularly interesting and potentially disrup- merous important physical quantities accessible to first tive applications of quantum information theory and of principles Monte Carlo simulations using classical com- quantum technologies lay within different scientific fields, puters. These include static properties, like masses and such as high-energy, nuclear, condensed matter physics or matrix elements, of baryons (such as protons and neu- chemistry[6]. Indeed, in the last years, it became increas- trons) and mesons (such as pions). Properties of the high- ingly clear that concepts and tools from quantum informa- temperature quark-gluon plasma in thermal equilibrium tion can unveil new directions and will most probably pro- are accessible as well. This includes, e.g., the critical tem- vide new tools to attack long-standing open problems such perature of the phase transition in which the chiral sym- as the study of information scrambling in black holes[7], metry of the quarks, which is spontaneously broken at low the solution of complex chemical or nuclear systems[8], temperatures, gets restored. After more than four decades or the study of lattice gauge theories (LGTs) { the main of intensive research, lattice QCD has matured to a very subject of this review. solid quantitative tool that is indispensable for correctly interpreting a large variety of experiments, including the LGTs are characterised by an extensive number of ones at the high-energy frontier of the Large Hadron Col- symmetries, that is, conservation laws that hold at ev- lider (LHC) at CERN. ery lattice site. They describe an incredibly vast variety of different phenomena that range from the fundamental However, there are other important aspects of the QCD interactions of matter at high energies [9] { the standard dynamics, both at high baryon density (such as in the model of particle physics { to the low-energy behaviour core of neutron stars) and for out-of-equilibrium real-time of some materials with normal and/or topological order evolution (such as the various stages of heavy-ion col- in condensed matter physics[10, 11]. Moreover, recently it lisions), where importance-sampling-based Monte Carlo has been shown that most of the hard problems in com- simulations fail due to very severe sign or complex action puter science can be recast as a LGT[12, 13]. The connec- problems. In these cases, reliable special purpose quantum tion passes through the recasting of the classical problem simulators or universal quantum computers may be the in Hamiltonian form, which generally assumes the form of only tools to successfully address these grand-challenge an Ising Hamiltonian with long-range disordered interac- problems. While immediate results with quantitative im- tions. This class of Hamiltonians can be mapped exactly pact on particle physics are unrealistic to hope for, a long- into two-dimensional LGT[14]. term investment in the exploration of quantum technolo- gies seems both timely and most interesting. Lattice gauge For all the aforementioned scenarios, quantum science theory has a very important role to play in this endeavour, provided two novel pathways to analyse them. The first because, besides fully-fledged lattice QCD, it provides a one has its root in Feynman's first intuition [15] of quan- large class of simpler models, in lower dimensions, with tum computers: having quantum hardware able to pre- simpler Abelian or non-Abelian gauge groups, or with a cisely reproduce another physical quantum model, allows modified matter content, which often are interesting also a powerful investigation tool for computing the observ- from a condensed matter perspective. The real-time evolu- ables of the model, and to verify or compare its prediction tion of all these models is as inaccessible to