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We propose fault-tolerant state preparation and decoding schemes that effectively convert every circuit-level error into an erasure error, leveraging the cluster state's high threshold against such errors. We find a set of codes for which such a conversion is possible, and study their performance against the standard circuit-level depolarizing model. Our best performing scheme, which is based on a concatenation with a classical code, improves the threshold by <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>16.5<\/mml:mn><mml:mi mathvariant=\"normal\">&amp;#x0025;<\/mml:mi><\/mml:math> and decreases the spacetime overhead by <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>32<\/mml:mn><mml:mi mathvariant=\"normal\">&amp;#x0025;<\/mml:mi><\/mml:math> compared to the scheme without concatenation, with each scheme subject to a physical error rate of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mn>10<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>&amp;#x2212;<\/mml:mo><mml:mn>3<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math> and achieving a logical error rate of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mn>10<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>&amp;#x2212;<\/mml:mo><mml:mn>6<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math>.<\/jats:p>","DOI":"10.22331\/q-2023-08-22-1089","type":"journal-article","created":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T14:17:49Z","timestamp":1692713869000},"page":"1089","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction"],"prefix":"10.22331","volume":"7","author":[{"given":"Zhaoyi","family":"Li","sequence":"first","affiliation":[{"name":"Department of Physics, Stanford University, Stanford, CA 94305, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Isaac","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of California, Davis, CA 95616, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrick","family":"Hayden","sequence":"additional","affiliation":[{"name":"Department of Physics, Stanford University, Stanford, CA 94305, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,8,22]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Dorit Aharonov and Michael Ben-Or. 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