Classical spin systems and the quantum stabilizer formalism: general mappings and applications

摘要

We present general mappings between classical spin systems and quantumphysics. More precisely, we show how to express partition functions andcorrelation functions of arbitrary classical spin models as inner productsbetween quantum stabilizer states and product states, thereby generalizingmappings for some specific models established in [Phys. Rev. Lett. 98, 117207(2007)]. For Ising- and Potts-type models with and without external magneticfield, we show how the entanglement features of the corresponding stabilizerstates are related to the interaction pattern of the classical model, while thechoice of product states encodes the details of interaction. These mappingsestablish a link between the fields of classical statistical mechanics andquantum information theory, which we utilize to transfer techniques and methodsdeveloped in one field to gain insight into the other. For example, we usequantum information techniques to recover well known duality relations andlocal symmetries of classical models in a simple way, and provide new classicalsimulation methods to simulate certain types of classical spin models. We showthat in this way all inhomogeneous models of q-dimensional spins with pairwiseinteraction pattern specified by a graph of bounded tree-width can be simulatedefficiently. Finally, we show relations between classical spin models andmeasurement-based quantum computation.