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In this work, we explore the remarkably powerful formalism of detector error models, which fully captures fault-tolerance at the circuit level. We introduce the detector error model formalism in a pedagogical manner and provide several examples. Additionally, we apply the formalism to three different levels of abstraction in the engineering cycle of fault-tolerant circuit designs: finding robust syndrome extraction circuits, identifying efficient measurement schedules, and constructing fault-tolerant procedures. We enhance the surface code&amp;apos;s resistance to measurement errors, devise short measurement schedules for color codes, and implement a more efficient fault-tolerant method for measuring logical operators.<\/jats:p>","DOI":"10.22331\/q-2025-11-06-1905","type":"journal-article","created":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T13:56:06Z","timestamp":1762437366000},"page":"1905","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Designing fault-tolerant circuits using detector error models"],"prefix":"10.22331","volume":"9","author":[{"given":"Peter-Jan H.S.","family":"Derks","sequence":"first","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alex","family":"Townsend-Teague","sequence":"additional","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ansgar G.","family":"Burchards","sequence":"additional","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jens","family":"Eisert","sequence":"additional","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"},{"name":"Helmholtz-Zentrum Berlin f\u00fcr Materialien und Energie, 14109 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2025,11,6]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. 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