Fast quantum codes based on Pauli block jacket matrices

  • Authors:

  • Ying Guo;Jun Peng;Moon Ho Lee

  • Affiliations:

  • School of Information Science and Engineering, Central South University, Changsha, China 410083;School of Information Science and Engineering, Central South University, Changsha, China 410083;Department of Information & Communication Engineering, Chonbuk National University, Chonju, Korea 561-756

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2009

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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.