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Effect of quantum fluctuation in error-correcting codes

Yosuke Otsubo

Jun-ichi Inoue

Kenji Nagata

Masato Okada*

  • Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-5861, Japan

  • Complex Systems Engineering, Graduate School of Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan

  • Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-5861, Japan

  • Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-5861, Japan and Brain Science Institute, RIKEN, Wako, Saitama 351-0198, Japan

  • *okada@mns.k.u-tokyo.ac.jp
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Phys. Rev. E 86, 051138 – Published 30 November, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.051138

Abstract

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.

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Phys. Rev. E 86, 051138– Published 30 November, 2012
  • Received 2 April 2012

©2012 American Physical Society

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