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Quantum error-correction codes<jats:sup>2<\/jats:sup> present a way to reach this goal by encoding logical information redundantly into many physical qubits. A key challenge in implementing such codes is accurately decoding noisy syndrome information extracted from redundancy checks to obtain the correct encoded logical information. Here we develop a recurrent, transformer-based neural network that learns to decode the surface code, the leading quantum error-correction code<jats:sup>3<\/jats:sup>. Our decoder outperforms other state-of-the-art decoders on real-world data from Google\u2019s Sycamore quantum processor for distance-3 and distance-5 surface codes<jats:sup>4<\/jats:sup>. On distances up to 11, the decoder maintains its advantage on simulated data with realistic noise including cross-talk and leakage, utilizing soft readouts and leakage information. After training on approximate synthetic data, the decoder adapts to the more complex, but unknown, underlying error distribution by training on a limited budget of experimental samples. Our work illustrates the ability of machine learning to go beyond human-designed algorithms by learning from data directly, highlighting machine learning as a strong contender for decoding in quantum computers.<\/jats:p>","DOI":"10.1038\/s41586-024-08148-8","type":"journal-article","created":{"date-parts":[[2024,11,20]],"date-time":"2024-11-20T16:04:23Z","timestamp":1732118663000},"page":"834-840","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":58,"title":["Learning high-accuracy error decoding for quantum processors"],"prefix":"10.1038","volume":"635","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3189-9162","authenticated-orcid":false,"given":"Johannes","family":"Bausch","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2401-5691","authenticated-orcid":false,"given":"Andrew W.","family":"Senior","sequence":"additional","affiliation":[]},{"given":"Francisco J. 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