Effect of quantum fluctuation in error-correcting codes.

We discuss the decoding performance of error-correcting codes based on a model in which quantum fluctuations are introduced by means of a transverse field. The essential issue in this paper is whether quantum fluctuations improve the decoding quality compared with the conventional estimation based on thermal fluctuations, which is called finite-temperature decoding. We found that an estimation incorporating quantum fluctuations approaches the optimal performance of finite-temperature decoding. The results are illustrated by numerically solving saddle-point equations and performing a Monte Carlo simulation. We also evaluated the upper bound of the overlap between the original sequence and the decoded sequence derived from the equations of state for the order parameters, which is a measure of the decoding performance.