Title :
Sparse-graph codes for quantum error correction
Author :
MacKay, David J C ; Mitchison, Graeme ; McFadden, Paul L.
Author_Institution :
Dept. of Phys., Cavendish Lab., Cambridge, UK
Abstract :
Sparse-graph codes appropriate for use in quantum error-correction are presented. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse-graph codes keep the number of quantum interactions associated with the quantum error-correction process small: a constant number per quantum bit, independent of the block length. Third, sparse-graph codes often offer great flexibility with respect to block length and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.
Keywords :
block codes; channel coding; decoding; error correction codes; graph theory; parity check codes; quantum computing; sparse matrices; block length; classical channel; probabilistic decoding; quantum error-correction; sparse-graph code; Decoding; Error correction codes; Geometry; Information rates; Information theory; Laboratories; Noise level; Parity check codes; Physics; Quantum mechanics; Error-correction codes; probabilistic decoding; quantum error correction;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2004.834737
