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To this end, we relate such circuits to discrete fixed-point path integrals in Euclidean spacetime, which describe the underlying topological order: If we fix a history of measurement outcomes, we obtain a fixed-point path integral carrying a pattern of topological defects. As an example, we show that the stabilizer toric code, subsystem toric code, and CSS Floquet code can be viewed as one and the same code on different spacetime lattices, and the honeycomb Floquet code is equivalent to the CSS Floquet code under a change of basis. We also use our formalism to derive two new error-correcting codes, namely a Floquet version of the 3<\/mml:mn>+<\/mml:mo>1<\/mml:mn><\/mml:math>-dimensional toric code using only 2-body measurements, as well as a dynamic code based on the double-semion string-net path integral.<\/jats:p>","DOI":"10.22331\/q-2024-03-20-1288","type":"journal-article","created":{"date-parts":[[2024,3,20]],"date-time":"2024-03-20T13:38:31Z","timestamp":1710941911000},"page":"1288","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["Topological error correcting processes from fixed-point path integrals"],"prefix":"10.22331","volume":"8","author":[{"given":"Andreas","family":"Bauer","sequence":"first","affiliation":[{"name":"Freie Universit\u00e4t Berlin, Arnimallee 14, 14195 Berlin, Germany"}]}],"member":"9598","published-online":{"date-parts":[[2024,3,20]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A. 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