A quantum information approach to statistical mechanics

Abstract: We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proofs of these two results are based on a mapping from partition functions to quantum states and to quantum circuits, respectively. Finally, we show how classical spin models can be used to describe certain fluctuating lattices appearing in models of discrete quantum gravity.