Fast quantum codes based on Pauli block jacket matrices

Fast quantum codes based on Pauli block jacket matrices 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Fast quantum codes based on Pauli block jacket matrices

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Publisher
Springer Journals
Copyright
Copyright © 2009 by The Author(s)
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-009-0113-1
Publisher site
See Article on Publisher Site

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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Apr 28, 2009

References

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