Clifford Code Constructions of Operator Quantum Error-Correcting Codes

Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This correspondence introduces a natural construction of such codes in terms of Clifford codes, an elegant generalization...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 54; no. 12; pp. 5760 - 5765
Main Authors: Klappenecker, A., Sarvepalli, P.K.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.12.2008
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Additives
Applied mathematics
Applied sciences
Clifford codes
Codes
Coding, codes
Construction
Convolution
Convolutional codes
Electrical engineering
Error analysis
Error correction
Error correction codes
Exact sciences and technology
Information theory
Information, signal and communications theory
Lattices
Mathematical analysis
Maximum likelihood decoding
Maximum likelihood detection
operator quantum error-correcting codes
Operators
quantum codes
Quantum physics
Signal and communications theory
Signal processing
Signal processing algorithms
stabilizer codes
State-space methods
Subspaces
subsystem codes
Telecommunications and information theory
Viterbi algorithm
quantum codes
Finite field
stabilizer codes
Clifford codes
Orthogonal code
Subsystem
operator quantum error-correcting codes
Subspace method
subsystem codes
Error correcting code
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This correspondence introduces a natural construction of such codes in terms of Clifford codes, an elegant generalization of stabilizer codes due to Knill. Character-theoretic methods are used to derive a simple method to construct operator quantum error-correcting codes from any classical additive code over a finite field, which obviates the need for self-orthogonal codes.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2008.2006429