Degenerate Quantum LDPC Codes With Good Finite Length Performance

We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the help of OSD-like post-processing the performance of the standa...

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Autores principales:	Pavel Panteleev, Gleb Kalachev
Formato:	article
Lenguaje:	EN
Publicado:	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/060e07c8e50546a49e200f091b1c6bb8
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spelling	oai:doaj.org-article:060e07c8e50546a49e200f091b1c6bb82021-11-22T14:01:30ZDegenerate Quantum LDPC Codes With Good Finite Length Performance2521-327X10.22331/q-2021-11-22-585https://doaj.org/article/060e07c8e50546a49e200f091b1c6bb82021-11-01T00:00:00Zhttps://quantum-journal.org/papers/q-2021-11-22-585/pdf/https://doaj.org/toc/2521-327XWe study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude. Using this new BP-OSD decoder we study the performance of several known classes of degenerate QLDPC codes including hypergraph product codes, hyperbicycle codes, homological product codes, and Haah's cubic codes. We also construct several interesting examples of short generalized bicycle codes. Some of them have an additional property that their syndromes are protected by small BCH codes, which may be useful for the fault-tolerant syndrome measurement. We also propose a new large family of QLDPC codes that contains the class of hypergraph product codes, where one of the used parity-check matrices is square. It is shown that in some cases such codes have better performance than hypergraph product codes. Finally, we demonstrate that the performance of the proposed BP-OSD decoder for some of the constructed codes is better than for a relatively large surface code decoded by a near-optimal decoder.Pavel PanteleevGleb KalachevVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenarticlePhysicsQC1-999ENQuantum, Vol 5, p 585 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Pavel Panteleev Gleb Kalachev Degenerate Quantum LDPC Codes With Good Finite Length Performance
description	We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude. Using this new BP-OSD decoder we study the performance of several known classes of degenerate QLDPC codes including hypergraph product codes, hyperbicycle codes, homological product codes, and Haah's cubic codes. We also construct several interesting examples of short generalized bicycle codes. Some of them have an additional property that their syndromes are protected by small BCH codes, which may be useful for the fault-tolerant syndrome measurement. We also propose a new large family of QLDPC codes that contains the class of hypergraph product codes, where one of the used parity-check matrices is square. It is shown that in some cases such codes have better performance than hypergraph product codes. Finally, we demonstrate that the performance of the proposed BP-OSD decoder for some of the constructed codes is better than for a relatively large surface code decoded by a near-optimal decoder.
format	article
author	Pavel Panteleev Gleb Kalachev
author_facet	Pavel Panteleev Gleb Kalachev
author_sort	Pavel Panteleev
title	Degenerate Quantum LDPC Codes With Good Finite Length Performance
title_short	Degenerate Quantum LDPC Codes With Good Finite Length Performance
title_full	Degenerate Quantum LDPC Codes With Good Finite Length Performance
title_fullStr	Degenerate Quantum LDPC Codes With Good Finite Length Performance
title_full_unstemmed	Degenerate Quantum LDPC Codes With Good Finite Length Performance
title_sort	degenerate quantum ldpc codes with good finite length performance
publisher	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
publishDate	2021
url	https://doaj.org/article/060e07c8e50546a49e200f091b1c6bb8
work_keys_str_mv	AT pavelpanteleev degeneratequantumldpccodeswithgoodfinitelengthperformance AT glebkalachev degeneratequantumldpccodeswithgoodfinitelengthperformance
_version_	1718417534986747904

Degenerate Quantum LDPC Codes With Good Finite Length Performance

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