Local Probabilistic Decoding of a Quantum Code Article Swipe
Thomas R. Scruby
,
Kae Nemoto
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.06985
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.06985
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser) which are uncorrectable for this decoder, so previous studies have considered modified versions of flip, sometimes in conjunction with other decoders. We argue that this may not always be necessary, and present numerical evidence for the existence of a threshold for flip when applied to the looplike syndromes of a three-dimensional toric code on a cubic lattice. This result can be attributed to the fact that the lowest-weight uncorrectable errors for this decoder are closer (in terms of Hamming distance) to correctable errors than to other uncorrectable errors, and so they are likely to become correctable in future code cycles after transformation by additional noise. Introducing randomness into the decoder can allow it to correct these "uncorrectable" errors with finite probability, and for a decoding strategy that uses a combination of belief propagation and probabilistic flip we observe a threshold of $\sim5.5\%$ under phenomenological noise. This is comparable to the best known threshold for this code ($\sim7.1\%$) which was achieved using belief propagation and ordered statistics decoding [Higgott and Breuckmann, 2022], a strategy with a runtime of $O(n^3)$ as opposed to the $O(n)$ ($O(1)$ when parallelised) runtime of our local decoder. We expect that this strategy could be generalised to work well in other low-density parity check codes, and hope that these results will prompt investigation of other previously overlooked decoders.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2212.06985
- https://arxiv.org/pdf/2212.06985
- OA Status
- green
- References
- 33
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4311641992
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https://openalex.org/W4311641992Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2212.06985Digital Object Identifier
- Title
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Local Probabilistic Decoding of a Quantum CodeWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
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2022-12-14Full publication date if available
- Authors
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Thomas R. Scruby, Kae NemotoList of authors in order
- Landing page
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https://arxiv.org/abs/2212.06985Publisher landing page
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https://arxiv.org/pdf/2212.06985Direct link to full text PDF
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YesWhether a free full text is available
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-
greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2212.06985Direct OA link when available
- Concepts
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Decoding methods, Algorithm, Probabilistic logic, Computer science, Belief propagation, Code (set theory), Hamming code, Randomness, Noise (video), Mathematics, Block code, Statistics, Image (mathematics), Programming language, Set (abstract data type), Artificial intelligenceTop concepts (fields/topics) attached by OpenAlex
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| abstract_inverted_index.cubic | 93 |
| abstract_inverted_index.exist | 29 |
| abstract_inverted_index.flip, | 52 |
| abstract_inverted_index.great | 15 |
| abstract_inverted_index.known | 189 |
| abstract_inverted_index.local | 7, 227 |
| abstract_inverted_index.other | 57, 123, 241, 255 |
| abstract_inverted_index.terms | 114 |
| abstract_inverted_index.there | 28 |
| abstract_inverted_index.these | 153, 249 |
| abstract_inverted_index.toric | 89 |
| abstract_inverted_index.under | 180 |
| abstract_inverted_index.using | 198 |
| abstract_inverted_index.which | 10, 38, 195 |
| abstract_inverted_index.$O(n)$ | 220 |
| abstract_inverted_index.2022], | 208 |
| abstract_inverted_index.always | 65 |
| abstract_inverted_index.become | 132 |
| abstract_inverted_index.belief | 169, 199 |
| abstract_inverted_index.closer | 112 |
| abstract_inverted_index.codes, | 245 |
| abstract_inverted_index.codes. | 22 |
| abstract_inverted_index.cycles | 137 |
| abstract_inverted_index.effect | 16 |
| abstract_inverted_index.errors | 31, 107, 120, 155 |
| abstract_inverted_index.expect | 230 |
| abstract_inverted_index.finite | 157 |
| abstract_inverted_index.future | 135 |
| abstract_inverted_index.likely | 130 |
| abstract_inverted_index.noise. | 142, 182 |
| abstract_inverted_index.parity | 243 |
| abstract_inverted_index.prompt | 252 |
| abstract_inverted_index.result | 96 |
| abstract_inverted_index.simple | 4 |
| abstract_inverted_index.($O(1)$ | 221 |
| abstract_inverted_index.Hamming | 116 |
| abstract_inverted_index.applied | 24, 81 |
| abstract_inverted_index.certain | 18 |
| abstract_inverted_index.classes | 19 |
| abstract_inverted_index.correct | 152 |
| abstract_inverted_index.decoder | 9, 110, 147 |
| abstract_inverted_index.errors, | 125 |
| abstract_inverted_index.observe | 175 |
| abstract_inverted_index.opposed | 217 |
| abstract_inverted_index.ordered | 202 |
| abstract_inverted_index.present | 69 |
| abstract_inverted_index.quantum | 26 |
| abstract_inverted_index.results | 250 |
| abstract_inverted_index.runtime | 213, 224 |
| abstract_inverted_index.studies | 46 |
| abstract_inverted_index.$O(n^3)$ | 215 |
| abstract_inverted_index.[Higgott | 205 |
| abstract_inverted_index.achieved | 197 |
| abstract_inverted_index.decoder, | 43 |
| abstract_inverted_index.decoder. | 228 |
| abstract_inverted_index.decoding | 162, 204 |
| abstract_inverted_index.evidence | 71 |
| abstract_inverted_index.lattice. | 94 |
| abstract_inverted_index.looplike | 84 |
| abstract_inverted_index.modified | 49 |
| abstract_inverted_index.previous | 45 |
| abstract_inverted_index.strategy | 163, 210, 233 |
| abstract_inverted_index.versions | 50 |
| abstract_inverted_index.classical | 8, 21 |
| abstract_inverted_index.decoders. | 58, 258 |
| abstract_inverted_index.distance) | 117 |
| abstract_inverted_index.existence | 74 |
| abstract_inverted_index.extremely | 3 |
| abstract_inverted_index.maximally | 6 |
| abstract_inverted_index.numerical | 70 |
| abstract_inverted_index.sometimes | 53 |
| abstract_inverted_index.syndromes | 85 |
| abstract_inverted_index.threshold | 77, 177, 190 |
| abstract_inverted_index.additional | 141 |
| abstract_inverted_index.attributed | 99 |
| abstract_inverted_index.comparable | 185 |
| abstract_inverted_index.considered | 48 |
| abstract_inverted_index.necessary, | 67 |
| abstract_inverted_index.overlooked | 257 |
| abstract_inverted_index.previously | 256 |
| abstract_inverted_index.randomness | 144 |
| abstract_inverted_index.statistics | 203 |
| abstract_inverted_index.$\sim5.5\%$ | 179 |
| abstract_inverted_index.Breuckmann, | 207 |
| abstract_inverted_index.Introducing | 143 |
| abstract_inverted_index.combination | 167 |
| abstract_inverted_index.conjunction | 55 |
| abstract_inverted_index.correctable | 119, 133 |
| abstract_inverted_index.generalised | 236 |
| abstract_inverted_index.low-density | 242 |
| abstract_inverted_index.propagation | 170, 200 |
| abstract_inverted_index.stabiliser) | 37 |
| abstract_inverted_index.probability, | 158 |
| abstract_inverted_index.($\sim7.1\%$) | 194 |
| abstract_inverted_index.investigation | 253 |
| abstract_inverted_index.lowest-weight | 105 |
| abstract_inverted_index.parallelised) | 223 |
| abstract_inverted_index.probabilistic | 172 |
| abstract_inverted_index.uncorrectable | 40, 106, 124 |
| abstract_inverted_index.transformation | 139 |
| abstract_inverted_index."uncorrectable" | 154 |
| abstract_inverted_index.constant-weight | 30 |
| abstract_inverted_index.phenomenological | 181 |
| abstract_inverted_index.three-dimensional | 88 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/16 |
| sustainable_development_goals[0].score | 0.41999998688697815 |
| sustainable_development_goals[0].display_name | Peace, Justice and strong institutions |
| citation_normalized_percentile.value | 0.14862345 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |