  We use quantum link models to construct a quantum simulator for U(N) and
SU(N) lattice gauge theories. These models replace Wilson's classical link
variables by quantum link operators, reducing the link Hilbert space to a
finite number of dimensions. We show how to embody these quantum link models
with fermionic matter with ultracold alkaline-earth atoms using optical
lattices. Unlike classical simulations, a quantum simulator does not suffer
from sign problems and can thus address the corresponding dynamics in real
time. Using exact diagonalization results we show that these systems share
qualitative features with QCD, including chiral symmetry breaking and we study
the expansion of a chirally restored region in space in real time.
