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Quantum Information Processing

, Volume 8, Issue 5, pp 361–378 | Cite as

Fast quantum codes based on Pauli block jacket matrices

  • Ying Guo
  • Jun Peng
  • Moon Ho Lee
Open Access
Article

Abstract

Jacket matrices motivated by the center weight Hadamard matrices have played an important role in signal processing, communications, image compression, cryptography, etc. In this paper, we suggest a design approach for the Pauli block jacket matrix achieved by substituting some Pauli matrices for all elements of common matrices. Since, the well-known Pauli matrices have been widely utilized for quantum information processing, the large-order Pauli block jacket matrix that contains commutative row operations are investigated in detail. After that some special Abelian groups are elegantly generated from any independent rows of the yielded Pauli block jacket matrix. Finally, we show how the Pauli block jacket matrix can simplify the coding theory of quantum error-correction. The quantum codes we provide do not require the dual-containing constraint necessary for the standard quantum error-correction codes, thus allowing us to construct quantum codes of the large codeword length. The proposed codes can be constructed structurally by using the stabilizer formalism of Abelian groups whose generators are selected from the row operations of the Pauli block jacket matrix, and hence have advantages of being fast constructed with the asymptotically good behaviors.

Keywords

Pauli block matrix Block jacket transform Pauli matrices Abelian group Quantum error-correction codes 

PACS

03.65.Bz 89.70.+c 

Notes

Acknowledgments

The authors are grateful to the anonymous referees for their detailed suggestions. This work was supported by Natural Science Foundation of Hunan Province (Nos. 07JJ3128, 2008RS4016), Postdoctoral Science Foundation of China (Nos. 20070420184, 200801341), and in part by Joint Project KOSEF/NSFC Korea Research Foundation KRF-2007-521-D00330, Chonbuk National University, Korea.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaChina
  2. 2.Department of Information & Communication EngineeringChonbuk National UniversityChonjuKorea

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