Quantum Spin Glasses Quantum Annealing, and Probabilistic Information Processing

Abstract

Recently, problems of information processing were investigated from the statistical mechanical point of view [1]. Among them, image restoration (see [2–4] and references therein) and error-correcting codes [5] are most suitable subjects. In the field of error-correcting codes, Sourlas [5] showed that the convolution codes can be constructed by an infinite range spin-glass Hamiltonian and the decoded message should correspond to the zero temperature spin configuration of the Hamiltonian. Ruján [6] suggested that the error of each bit can be suppressed if one uses finite temperature equilibrium states (sign of the local magnetization) as the decoding result, what we call the MPM (maximizer of posterior marginal) estimate, instead of zero temperature spin configurations, and this optimality of the retrieval quality at a specific decoding temperature (this temperature is well known as the Nishimori temperature in the field of spin glasses) is proved by Nishimori [7].