  We discuss real-space lattice models equivalent to gauge theories with a
discrete non-Abelian gauge group. We construct the Hamiltonian formalism which
is appropriate for their solid-state physics implementation and outline their
basic properties. The unusual physics of these systems is due to local
constraints on the degrees of freedom which are variables localized on the
links of the lattice. We discuss two types of constraints that become
equivalent after a duality transformation for Abelian theories but are
qualitatively different for non-Abelian ones. We emphasize highly nontrivial
topological properties of the excitations (fluxons and charges) in these
non-Abelian discrete lattice gauge theories. We show that an implementation of
these models may provide one with the realization of an ideal quantum computer,
that is the computer that is protected from the noise and allows a full set of
precise manipulations required for quantum computations. We suggest a few
designs of the Josephson-junction arrays that provide the experimental
implementations of these models and discuss the physical restrictions on the
parameters of their junctions.
