Quantum Expander Codes

We present an efficient decoding algorithm for constant rate quantum hyper graph-product LDPC codes which provably corrects adversarial errors of weight proportional to the code minimum distance, or equivalently to the square-root of the block length. The algorithm runs in time linear in the number...

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Bibliographic Details
Published in2015 IEEE 56th Annual Symposium on Foundations of Computer Science pp. 810 - 824
Main Authors Leverrier, Anthony, Tillich, Jean-Pierre, Zemor, Gilles
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.10.2015
Subjects
CSS codes
Decoding
Expander codes
Generators
Graph theory
Iterative decoding
LDPC codes
quantum codes
Quantum computing
Robustness
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ISSN0272-5428
DOI10.1109/FOCS.2015.55

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Summary:We present an efficient decoding algorithm for constant rate quantum hyper graph-product LDPC codes which provably corrects adversarial errors of weight proportional to the code minimum distance, or equivalently to the square-root of the block length. The algorithm runs in time linear in the number of qubits, which makes its performance the strongest to date for linear-time decoding of quantum codes. The algorithm relies on expanding properties, not of the quantum code's factor graph directly, but of the factor graph of the original classical code it is constructed from.
ISSN:0272-5428
DOI:10.1109/FOCS.2015.55