Minimal Trellises for non-Degenerate and Degenerate Decoding of Quantum Stabilizer Codes
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| Publicado en: | arXiv.org (Oct 10, 2024), p. n/a |
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| Otros Autores: | , , |
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Cornell University Library, arXiv.org
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| Acceso en línea: | Citation/Abstract Full text outside of ProQuest |
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| 022 | |a 2331-8422 | ||
| 035 | |a 3115595236 | ||
| 045 | 0 | |b d20241010 | |
| 100 | 1 | |a Stylianou, Evagoras | |
| 245 | 1 | |a Minimal Trellises for non-Degenerate and Degenerate Decoding of Quantum Stabilizer Codes | |
| 260 | |b Cornell University Library, arXiv.org |c Oct 10, 2024 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a 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. | |
| 653 | |a Algorithms | ||
| 653 | |a Maximum likelihood estimation | ||
| 653 | |a Complexity | ||
| 653 | |a Viterbi decoding | ||
| 653 | |a Maximum likelihood decoding | ||
| 653 | |a Viterbi algorithm detectors | ||
| 700 | 1 | |a Sidorenko, Vladimir | |
| 700 | 1 | |a Deppe, Christian | |
| 700 | 1 | |a Boche, Holger | |
| 773 | 0 | |t arXiv.org |g (Oct 10, 2024), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3115595236/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/2410.07897 |