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A possible application of such a paradigm is distributed quantum computation, where separate computing nodes work together on a fault-tolerant computation through entanglement. We gauge error thresholds of the architectures with an efficient stabilizer simulator to investigate the resilience against both circuit-level and network noise. We show that, for both monolithic (i.e., non-distributed) and distributed implementations, an architecture based on the diamond lattice may outperform the conventional cubic lattice. Moreover, the high erasure thresholds of non-cubic lattices may be exploited further in a distributed context, as their performance may be boosted through <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\">entanglement distillation<\/mml:mtext><\/mml:mrow><\/mml:math> by trading in entanglement success rates against erasure errors during the error-decoding process. These results highlight the significance of lattice geometry in the design of fault-tolerant measurement-based quantum computing on a network, emphasizing the potential for constructing robust and scalable distributed quantum computers.<\/jats:p>","DOI":"10.22331\/q-2025-05-05-1723","type":"journal-article","created":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T08:36:12Z","timestamp":1746434172000},"page":"1723","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Fault-tolerant structures for measurement-based quantum computation on a network"],"prefix":"10.22331","volume":"9","author":[{"given":"Yves","family":"van Montfort","sequence":"first","affiliation":[{"name":"QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S\u00e9bastian","family":"de Bone","sequence":"additional","affiliation":[{"name":"QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands"},{"name":"QuSoft, CWI, Science Park 123, 1098 XG Amsterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Elkouss","sequence":"additional","affiliation":[{"name":"QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands"},{"name":"Networked Quantum Devices Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,5,5]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"K. 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