Unified Quantum Convolutional Coding

Details Unified Quantum Convolutional Coding Unified Quantum Convolutional Coding

2008-01-06

arxiv.org/abs/0801.0821v2

Proceedings of the 2008 International Symposium on Information Theory, pp. 359-363, Toronto, Ontario, Canada, July 2008.

Physics

Quantum Physics

5 pages, 1 figure, Accepted for publication in the Proceedings of the 2008 IEEE International Symposium on Information Theory

Scientific paper

10.1109/ISIT.2008.4595008

We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum channel for sending classical and quantum information simultaneously. Our method incorporates several resources for quantum redundancy: fresh ancilla qubits, entangled bits, and gauge qubits. The use of these diverse resources gives our technique the benefits of both active and passive quantum error correction. We can encode a classical-quantum bit stream with periodic quantum gates because our codes possess a convolutional structure. We end with an example of a ``grandfather'' quantum convolutional code that protects one qubit and one classical bit per frame by encoding them with one fresh ancilla qubit, one entangled bit, and one gauge qubit per frame. We explicitly provide the encoding and decoding circuits for this example.

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