{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T17:19:03Z","timestamp":1778174343722,"version":"3.51.4"},"reference-count":28,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2020,8,24]],"date-time":"2020-08-24T00:00:00Z","timestamp":1598227200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We still do not have perfect decoders for topological codes that can satisfy all needs of different experimental setups. Recently, a few neural network based decoders have been studied, with the motivation that they can adapt to a wide range of noise models, and can easily run on dedicated chips without a full-fledged computer. The later feature might lead to fast speed and the ability to operate at low temperatures. However, a question which has not been addressed in previous works is whether neural network decoders can handle 2D topological codes with large distances. In this work, we provide a positive answer for the toric code \\cite{Kitaev2003Faulttolerantanyon}. The structure of our neural network decoder is inspired by the renormalization group decoder \\cite{duclos2010fast, duclos2013fault}. With a fairly strict policy on training time, when the bit-flip error rate is lower than<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>9<\/mml:mn><mml:mi mathvariant=\"normal\">%<\/mml:mi><\/mml:math>and syndrome extraction is perfect, the neural network decoder performs better when code distance increases. With a less strict policy, we find it is not hard for the neural decoder to achieve a performance close to the minimum-weight perfect matching algorithm. The numerical simulation is done up to code distance<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>64<\/mml:mn><\/mml:math>. Last but not least, we describe and analyze a few failed approaches. They guide us to the final design of our neural decoder, but also serve as a caution when we gauge the versatility of stock deep neural networks. The source code of our neural decoder can be found at \\cite{sourcecodegithub}.<\/jats:p>","DOI":"10.22331\/q-2020-08-24-310","type":"journal-article","created":{"date-parts":[[2020,8,24]],"date-time":"2020-08-24T16:34:53Z","timestamp":1598286893000},"page":"310","source":"Crossref","is-referenced-by-count":28,"title":["Neural Network Decoders for Large-Distance 2D Toric Codes"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1806-9391","authenticated-orcid":false,"given":"Xiaotong","family":"Ni","sequence":"first","affiliation":[{"name":"QuTech, Delft University of Technology, P.O.Box 5046, 2600 GA Delft, The Netherlands."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2020,8,24]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A.Yu. Kitaev. Fault-tolerant quantum computation by anyons. 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