Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes

Details Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes

2006-02-15

arxiv.org/abs/quant-ph/0602129v1

Proceedings 2006 IEEE International Symposium on Information Theory, pp. 1109-1113

Physics

Quantum Physics

6 pages, 1 figure, submitted to 2006 IEEE International Symposium on Information Theory

Scientific paper

10.1109/ISIT.2006.261956

We present an algorithm to construct quantum circuits for encoding and inverse encoding of quantum convolutional codes. We show that any quantum convolutional code contains a subcode of finite index which has a non-catastrophic encoding circuit. Our work generalizes the conditions for non-catastrophic encoders derived in a paper by Ollivier and Tillich (quant-ph/0401134) which are applicable only for a restricted class of quantum convolutional codes. We also show that the encoders and their inverses constructed by our method naturally can be applied online, i.e., qubits can be sent and received with constant delay.

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