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Published November 2008 | public
Journal Article

On the iterative decoding of sparse quantum codes

Abstract

We address the problem of decoding sparse quantum error correction codes. For Pauli channels, this task can be accomplished by a version of the belief propagation algorithm used for decoding sparse classical codes. Quantum codes pose two new challenges however. Firstly, their Tanner graph unavoidably contain small loops which typically undermines the performance of belief propagation. Secondly, sparse quantum codes are by definition highly degenerate. The standard belief propagation algorithm does not exploit this feature, but rather it is impaired by it. We propose heuristic methods to improve belief propagation decoding, specifically targeted at these two problems. While our results exhibit a clear improvement due to the proposed heuristic methods, they also indicate that the main source of errors in the quantum coding scheme remains in the decoding.

Additional Information

© 2008 Rinton Press. Received December 31, 2007. Revised July 1, 2008. Communicated by: H-K Lo & M Mosca. We are grateful to H. Ollivier for valuable comments and useful discussions. DP is supported in part by the Gordon and Betty Moore Foundation through Caltech's Center for the Physics of Information, by the National Science Foundation under Grant No. PHY-0456720, and by the Natural Sciences and Engineering Research Council of Canada. YC is supported by University Research Council of Southern Methodist University.

Additional details

Created:
August 22, 2023
Modified:
October 18, 2023