Quantum Convolutional BCH Codes

Details Quantum Convolutional BCH Codes Quantum Convolutional BCH Codes

2007-03-13

arxiv.org/abs/quant-ph/0703113v2

Proceedings 2007 Canadian Workshop on Information Theory (CWIT 2007), Edmonton, Canada, June 2007, pp. 180-183

Physics

Quantum Physics

4 pages, minor changes, accepted for publication at the 10th Canadian Workshop on Information Theory (CWIT'07)

Scientific paper

10.1109/CWIT.2007.375730

Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. We introduce two new families of quantum convolutional codes. Our construction is based on an algebraic method which allows to construct classical convolutional codes from block codes, in particular BCH codes. These codes have the property that they contain their Euclidean, respectively Hermitian, dual codes. Hence, they can be used to define quantum convolutional codes by the stabilizer code construction. We compute BCH-like bounds on the free distances which can be controlled as in the case of block codes, and establish that the codes have non-catastrophic encoders.

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