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The two key novelties are (i) the introduction of a lattice defect in the underlying cluster state and (ii) the use of the Rudolph-Grover rebit encoding. Concretely, (i) allows for a topological implementation of the Hadamard gate, while (ii) does the same for the phase gate. Furthermore, we develop general ideas towards circuit compaction and algorithmic circuit verification, which we implement for the Reed-Muller code used for magic state distillation. Our performance analysis highlights the overall improvements provided by the new methods.<\/jats:p>","DOI":"10.22331\/q-2026-02-06-1997","type":"journal-article","created":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T13:33:50Z","timestamp":1770384830000},"page":"1997","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["A 3D lattice defect and efficient computations in topological MBQC"],"prefix":"10.22331","volume":"10","author":[{"given":"Gabrielle","family":"Tournaire","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, University of British Columbia Vancouver, Canada"},{"name":"Stewart Blusson Quantum Matter Institute, University of British Columbia Vancouver, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marvin","family":"Schwiering","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Raussendorf","sequence":"additional","affiliation":[{"name":"Stewart Blusson Quantum Matter Institute, University of British Columbia Vancouver, Canada"},{"name":"Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sven","family":"Bachmann","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of British Columbia Vancouver, Canada"},{"name":"Department of Mathematics, University of British Columbia Vancouver, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2026,2,6]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. 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