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.Graphical abstract
Highlights
In the last few decades, quantum information theory has been fast developing and its application to the real world has spawned different technologies that – as for classical information theory – encompass the fields of communication, computation, sensing, and simulation [1–3]
In the last years, it became increasingly clear that concepts and tools from quantum information can unveil new directions and will most probably provide new tools to attack long-standing open problems such as the study of information scrambling in black holes [7], the solution of complex chemical or nuclear systems [8], or the study of lattice gauge theories (LGTs) – the main subject of this review
The aim was to understand the robustness of topological phases of matter in the presence of interactions, a problem that poses a difficult challenge in modern condensed matter physics, showing interesting connections to high-energy physics (see other works facilitating quantum simulations with ultra-cold atoms and ions: Junemann et al [247] for exploration of interacting topological insulators with ultra-cold atoms in the synthetic Creutz-Hubbard model, Magnifico et al [248] for symmetry-protected topological phases in lattice gauge theories, Magnifico et al [249] for the study of the topological Schwinger model, Gonzalez-Cuadra et al [250] for Z(N ) gauge theories coupled to topological fermions
Summary
In the last few decades, quantum information theory has been fast developing and its application to the real world has spawned different technologies that – as for classical information theory – encompass the fields of communication, computation, sensing, and simulation [1–3]. He introduced a hyper-cubic space-time lattice as a gauge invariant regulator of ultraviolet divergences, with quark fields residing on lattice sites and gluons fields residing on links connecting nearest-neighbour sites This framework makes numerous important physical quantities accessible to first principles Monte Carlo simulations using classical computers. There are other important aspects of the QCD dynamics, both at high baryon density (such as in the core of neutron stars) and for out-of-equilibrium real-time evolution (such as the various stages of heavy-ion collisions), where importance-sampling-based Monte Carlo simulations fail due to very severe sign or complex action problems In these cases, reliable special purpose quantum simulators or universal quantum computers may be the only tools to successfully address these grandchallenge problems. The first experimental realisations of these ideas are briefly mentioned
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
