  Using ultracold alkaline-earth atoms in optical lattices, we construct a
quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic
matter based on quantum link models. These systems share qualitative features
with QCD, including chiral symmetry breaking and restoration at non-zero
temperature or baryon density. Unlike classical simulations, a quantum
simulator does not suffer from sign problems and can address the corresponding
chiral dynamics in real time.
