{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T00:51:00Z","timestamp":1771894260832,"version":"3.50.1"},"reference-count":20,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T00:00:00Z","timestamp":1603843200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface code place qubits on a planar grid and assume native CNOT gates between the data qubits with nearest-neighbor ancilla qubits.Here, we present surface code error-correction schemes using <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">only<\/mml:mtext><\/mml:mrow><\/mml:math> Pauli measurements on single qubits and on pairs of nearest-neighbor qubits. In particular, we provide several qubit layouts that offer favorable trade-offs between qubit overhead, circuit depth and connectivity degree. We also develop minimized measurement sequences for syndrome extraction, enabling reduced logical error rates and improved fault-tolerance thresholds.Our work applies to topologically protected qubits realized with Majorana zero modes and to similar systems in which multi-qubit Pauli measurements rather than CNOT gates are the native operations.<\/jats:p>","DOI":"10.22331\/q-2020-10-28-352","type":"journal-article","created":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T11:06:16Z","timestamp":1603883176000},"page":"352","source":"Crossref","is-referenced-by-count":30,"title":["Optimization of the surface code design for Majorana-based qubits"],"prefix":"10.22331","volume":"4","author":[{"given":"Rui","family":"Chao","sequence":"first","affiliation":[{"name":"University of Southern California, Los Angeles, CA, USA"}]},{"given":"Michael E.","family":"Beverland","sequence":"additional","affiliation":[{"name":"Microsoft Quantum and Microsoft Research, Redmond, WA, USA"}]},{"given":"Nicolas","family":"Delfosse","sequence":"additional","affiliation":[{"name":"Microsoft Quantum and Microsoft Research, Redmond, WA, USA"}]},{"given":"Jeongwan","family":"Haah","sequence":"additional","affiliation":[{"name":"Microsoft Quantum and Microsoft Research, Redmond, WA, USA"}]}],"member":"9598","published-online":{"date-parts":[[2020,10,28]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A. 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