Minimal Trellises for non-Degenerate and Degenerate Decoding of Quantum Stabilizer Codes

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Detalles Bibliográficos
Publicado en:	arXiv.org (Oct 10, 2024), p. n/a
Autor Principal:	Stylianou, Evagoras
Outros autores:	Sidorenko, Vladimir, Deppe, Christian, Boche, Holger
Publicado:	Cornell University Library, arXiv.org
Materias:	Algorithms Maximum likelihood estimation Complexity Viterbi decoding Maximum likelihood decoding Viterbi algorithm detectors
Acceso en liña:	Citation/Abstract Full text outside of ProQuest
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Descripción
Resumo:	This paper presents a comprehensive guide to designing minimal trellises for both non-degenerate and degenerate decoding of quantum stabilizer codes. For non-degenerate decoding, various strategies are explored, leveraging insights from classical rectangular codes to minimize the complexity associated with the non-degenerate maximum likelihood error estimation using the Viterbi algorithm. Additionally, novel techniques for constructing minimal multi-goal trellises for degenerate decoding are introduced, including a merging algorithm, a Shannon-product approach, and the BCJR-Wolf method. The study establishes essential properties of multi-goal trellises and provides bounds on the decoding complexity using the sum-product Viterbi decoding algorithm. These advancements decrease the decoding complexity by a factor \(\mathcal{O}(n)\), where \(n\) is the code length. Finally, the paper applies these results to CSS codes and demonstrates a reduction in complexity by independently applying degenerate decoding to \(X\) and \(Z\) errors.
ISSN:	2331-8422
Fonte:	Engineering Database