  Abelian and non-Abelian gauge theories are of central importance in many
areas of physics. In condensed matter physics, Abelian U(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
non-perturbatively 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 from 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
suggests 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 collisions, first in
simpler model gauge theories and ultimately in QCD.
