Soft-decision decoder for quantum erasure and probabilistic-gate error models

Hayato Goto and Hironori Uchikawa
Phys. Rev. A 89, 022322 – Published 18 February 2014

Abstract

A soft-decision decoder for quantum erasure errors with standard depolarizing errors is proposed for concatenated Calderbank-Shor-Steane codes. This decoding is computationally efficient as long as the block size of each concatenation level is sufficiently small. The numerical simulation with a specific quantum code called the C4/C6 code shows that this decoder can achieve almost optimal performance and the so-called hashing bound for the erasure and depolarizing error model. Since probabilistic-gate errors can be regarded as erasure errors, this decoder is useful for fault-tolerant quantum computation with probabilistic gates. To demonstrate this, we perform numerical simulation with the C4/C6 code. Consequently, it turns out that the error probability of a logical controlled-not gate with probabilistic physical two-qubit gates is improved by three orders of magnitude by the present decoder compared to a previous hard-decision decoder.

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  • Received 30 September 2013

DOI:https://doi.org/10.1103/PhysRevA.89.022322

©2014 American Physical Society

Authors & Affiliations

Hayato Goto1 and Hironori Uchikawa2

  • 1Frontier Research Laboratory, Corporate Research & Development Center, Toshiba Corporation, 1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki-shi 212-8582, Japan
  • 2Center for Semiconductor Research & Development, Toshiba Corporation Semiconductor & Storage Products Company, 2-5-1, Kasama, Sakae-ku, Yokohama 247-8585, Japan

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Issue

Vol. 89, Iss. 2 — February 2014

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