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It has a short operation period of 4 steps and our performance analysis for a standard circuit noise model yields a high fault-tolerance threshold of approximately <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>0.66<\/mml:mn><mml:mi mathvariant=\"normal\">&amp;#x0025;<\/mml:mi><\/mml:math>. The syndrome extraction circuits avoid bidirectional hook errors, so we can achieve full code distance by choosing appropriate boundary conditions. We also construct variants of the syndrome extraction circuits that entirely prevent hook errors, at the cost of larger circuit depth. This achieves full distance regardless of boundary conditions, with only a modest decrease in the threshold. Furthermore, we propose an efficient strategy for dealing with dead components (qubits and measurements) in our surface code realization, which can be adopted more generally for other surface code realizations. This new surface code realization is highly optimized for Majorana-based hardware, accounting for constraints imposed by layouts and the implementation of measurements, making it competitive with the recently proposed Floquet codes.<\/jats:p>","DOI":"10.22331\/q-2024-08-02-1429","type":"journal-article","created":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T13:26:23Z","timestamp":1722605183000},"page":"1429","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["Improved Pairwise Measurement-Based Surface Code"],"prefix":"10.22331","volume":"8","author":[{"given":"Linnea","family":"Grans-Samuelsson","sequence":"first","affiliation":[{"name":"Microsoft Station Q, Santa Barbara, California 93106-6105 USA"}]},{"given":"Ryan V.","family":"Mishmash","sequence":"additional","affiliation":[{"name":"Microsoft Station Q, Santa Barbara, California 93106-6105 USA"}]},{"given":"David","family":"Aasen","sequence":"additional","affiliation":[{"name":"Microsoft Station Q, Santa Barbara, California 93106-6105 USA"}]},{"given":"Christina","family":"Knapp","sequence":"additional","affiliation":[{"name":"Microsoft Station Q, Santa Barbara, California 93106-6105 USA"}]},{"given":"Bela","family":"Bauer","sequence":"additional","affiliation":[{"name":"Microsoft Station Q, Santa Barbara, California 93106-6105 USA"}]},{"given":"Brad","family":"Lackey","sequence":"additional","affiliation":[{"name":"Microsoft Quantum, Redmond, Washington 98052, USA"}]},{"given":"Marcus P. da","family":"Silva","sequence":"additional","affiliation":[{"name":"Microsoft Quantum, Redmond, Washington 98052, USA"}]},{"given":"Parsa","family":"Bonderson","sequence":"additional","affiliation":[{"name":"Microsoft Station Q, Santa Barbara, California 93106-6105 USA"}]}],"member":"9598","published-online":{"date-parts":[[2024,8,2]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Alexei Yu. 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