Quantum codes based on fast pauli block transforms in the finite field

Quantum codes based on fast pauli block transforms in the finite field Motivated by the fast Pauli block transforms (or matrices) over the finite field GF(q) for an arbitrary number q, we suggest how to construct the simplified quantum code on the basis of quadratic residues. The present quantum code, which is the stabilizer quantum code, can be fast generated from an Abelian group with commutative quantum operators being selected from a suitable Pauli block matrix. This construction does not require the dual-containing or self-orthogonal constraint for the standard quantum error-correction code, thus allowing us to construct a quantum code with much efficiency. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum codes based on fast pauli block transforms in the finite field

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Publisher
Springer Journals
Copyright
Copyright © 2010 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/s11128-010-0171-4
Publisher site
See Article on Publisher Site

Abstract

Motivated by the fast Pauli block transforms (or matrices) over the finite field GF(q) for an arbitrary number q, we suggest how to construct the simplified quantum code on the basis of quadratic residues. The present quantum code, which is the stabilizer quantum code, can be fast generated from an Abelian group with commutative quantum operators being selected from a suitable Pauli block matrix. This construction does not require the dual-containing or self-orthogonal constraint for the standard quantum error-correction code, thus allowing us to construct a quantum code with much efficiency.

Journal

Quantum Information ProcessingSpringer Journals

Published: Mar 10, 2010

References

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