We are interested in an alternative approach to circuit-based quantum computation, premised on the notion that simulating interesting Hamiltonian systems can solve challenging computational problems. We focuse on a technique for preparing ground states of such Hamiltonians, by simulating their interaction with an infinitely large (yet very simple) 'bath'. So far we have shown that this approach can 'cool' highly degenerate Hamiltonian systems. When identifying the output groundstates as the results of conventional quantum algorithms, this approach scales favorably in terms of simulation cost. Another topic we are studying is non-equilibrium (quantum) statistical physics, and its relationship to quantum information science. Specifically, we are interested in heat flow in simple quantum systems and applications of the fluctuation theorems to quantities relevant to both thermodynamics (like entropy, heat and work) and information theory (like relative entropy, mutual information, and channel capacities).