  Many phenomena occurring in strongly correlated quantum systems still await
conclusive explanations. The absence of isolated free quarks in nature is an
example. It is attributed to quark confinement, whose origin is not yet
understood. The phase diagram for nuclear matter at general temperatures and
densities, studied in heavy-ion collisions, is not settled. Finally, we have no
definitive theory of high-temperature superconductivity. Though we have
theories that could underlie such physics, we lack the tools to determine the
experimental consequences of these theories. Quantum simulators may provide
such tools. Here we show how to engineer quantum simulators of non-Abelian
lattice gauge theories. The systems we consider have several applications: they
can be used to mimic quark confinement or to study dimer and valence-bond
states (which may be relevant for high-temperature superconductors).
