Abelian and non-Abelian gauge theories are of central importance\udin many areas of physics. In condensed matter physics, AbelianU(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev’s toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer\udfrom the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories\udsuggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion\udcollisions, first in simpler model gauge theories and ultimately\udin QCD.
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