Finite temperature quantum simulation of stabilizer Hamiltonians

We present a scheme for robust finite temperature quantum simulation of stabilizer Hamiltonians. The scheme is designed for realization in a physical system consisting of a finite set of neutral atoms trapped in an addressable optical lattice that are controllable via one- and two-body operations together with dissipative one-body operations such as optical pumping. We show that these minimal physical constraints suffice for design of a quantum simulation scheme for any stabilizer Hamiltonian at arbitrary temperature. We demonstrate the approach with application to the Abelian and non-Abelian toric codes.