  We present an architecture for the quantum simulation of many-body spin
interactions based on ultracold polar molecules trapped in optical lattices.
Our approach employs digital quantum simulation, i.e., the dynamics of the
simulated system is reproduced by the quantum simulator in a stroboscopic
pattern, and allows to simulate both coherent and dissipative dynamics. We
discuss the realization of Kitaev's toric code Hamiltonian, a paradigmatic
model involving four-body interactions, and we analyze the requirements for an
experimental implementation.
