Quantum simulation of many-body spin interactions with ultracold polar molecules

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 realisation of Kitaev's toric code Hamiltonian, a paradigmatic model involving four-body interactions, and analyse the requirements for an experimental implementation.