A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices

Lai, C; Lu, C

A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices

Lai, C Lu, C

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Publisher:: IEEE-Inst Electrical Electronics Engineers Inc
Publication Type:: Journal Article
Citation:: IEEE Transactions On Information Theory, 2011, 57 (10), pp. 7163 - 7179
Issue Date:: 2011-01

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Field	Value	Language
dc.contributor.author	Lai, C	en_US
dc.contributor.author	Lu, C	en_US
dc.date.issued	2011-01	en_US
dc.identifier.citation	IEEE Transactions On Information Theory, 2011, 57 (10), pp. 7163 - 7179	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/29702
dc.description.abstract	In this paper, a new but simple construction of stabilizer codes and related entanglement-assisted quantum error-correcting codes is proposed based on syndrome assignment by classical parity-check matrices. This method turns the construction of quantum stabilizer codes to the construction of classical parity-check matrices satisfying a specific commutative condition. The designed minimum distance 2t+1 of the constructed quantum stabilizer codes can be achieved by a commutative classical parity-check matrix with classical minimum distance 4t-m, where the parameter m, 0 = m = 2t, depends on a property of the parity-check matrix. As m decreases, there is an increasing set of additional correctable error operators beyond the designed error correcting capability t. The (asymptotic) coding efficiency is at least comparable to that of CSS codes. A class of quantum Reed-Muller codes is constructed and codes in this class have a larger set of correctable error operators than that of the quantum Reed-Muller codes previously developed in the literature. Quantum circulant codes are also constructed and many of them are optimal in terms of their coding parameters.	en_US
dc.publisher	IEEE-Inst Electrical Electronics Engineers Inc	en_US
dc.relation.ispartof	IEEE Transactions On Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2011.2165812	en_US
dc.rights	© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices	en_US
dc.type	Journal Article
utslib.citation.volume	10	en_US
utslib.citation.volume	57	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	1005 Communications Technologies	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access
pubs.consider-herdc	false	en_US
pubs.issue	10	en_US
pubs.volume	57	en_US

Abstract:

In this paper, a new but simple construction of stabilizer codes and related entanglement-assisted quantum error-correcting codes is proposed based on syndrome assignment by classical parity-check matrices. This method turns the construction of quantum stabilizer codes to the construction of classical parity-check matrices satisfying a specific commutative condition. The designed minimum distance 2t*+1 of the constructed quantum stabilizer codes can be achieved by a commutative classical parity-check matrix with classical minimum distance 4t*-m, where the parameter m, 0 = m = 2t*, depends on a property of the parity-check matrix. As m decreases, there is an increasing set of additional correctable error operators beyond the designed error correcting capability t*. The (asymptotic) coding efficiency is at least comparable to that of CSS codes. A class of quantum Reed-Muller codes is constructed and codes in this class have a larger set of correctable error operators than that of the quantum Reed-Muller codes previously developed in the literature. Quantum circulant codes are also constructed and many of them are optimal in terms of their coding parameters.

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http://hdl.handle.net/10453/29702