  We demonstrate how to build a simulation of two dimensional physical theories
describing topologically ordered systems whose excitations are in one to one
correspondence with irreducible representations of a Hopf algebra, D(G), the
quantum double of a finite group G. Our simulation uses a digital sequence of
operations on a spin lattice to prepare a ground "vacuum" state and to create,
braid and fuse anyonic excitations. The simulation works with or without the
presence of a background Hamiltonian though only in the latter case is the
system topologically protected. We describe a physical realization of a
simulation of the simplest non-Abelian model, D(S_3), using trapped neutral
atoms in a two dimensional optical lattice and provide a sequence of steps to
perform universal quantum computation with anyons. The use of ancillary spin
degrees of freedom figures prominently in our construction and provides a novel
technique to prepare and probe these systems.
