{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T22:30:38Z","timestamp":1765233038952},"reference-count":20,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2021,1,20]],"date-time":"2021-01-20T00:00:00Z","timestamp":1611100800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Magic state distillation uses special codes to suppress errors in input states, which are often tailored to a Clifford-twirled error model. We present detailed measurement sequences for magic state distillation protocols which can suppress arbitrary errors on any part of a protocol, assuming the independence of errors across qubits. Provided with input magic states, our protocol operates on a two-dimensional square grid by measurements of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>Z<\/mml:mi><mml:mi>Z<\/mml:mi><\/mml:math> on horizontal pairs of qubits, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>X<\/mml:mi><mml:mi>X<\/mml:mi><\/mml:math> on vertical pairs, and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>Z<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>X<\/mml:mi><\/mml:math> on single qubits.<\/jats:p>","DOI":"10.22331\/q-2021-01-20-383","type":"journal-article","created":{"date-parts":[[2021,1,20]],"date-time":"2021-01-20T17:24:30Z","timestamp":1611163470000},"page":"383","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Measurement sequences for magic state distillation"],"prefix":"10.22331","volume":"5","author":[{"given":"Jeongwan","family":"Haah","sequence":"first","affiliation":[{"name":"Microsoft Quantum, Redmond, Washington, USA"}]},{"given":"Matthew B.","family":"Hastings","sequence":"additional","affiliation":[{"name":"Microsoft Quantum, Santa Barbara, California, USA"},{"name":"Microsoft Quantum, Redmond, Washington, USA"}]}],"member":"9598","published-online":{"date-parts":[[2021,1,20]]},"reference":[{"key":"0","unstructured":"E. Knill, ``Fault-tolerant postselected quantum computation: Schemes,'' (2004a), arXiv:quant-ph\/0402171v1."},{"key":"1","unstructured":"E. Knill, ``Fault-tolerant postselected quantum computation: Threshold analysis,'' (2004b), arXiv:quant-ph\/0404104v1."},{"key":"2","doi-asserted-by":"publisher","unstructured":"P. Aliferis, D. Gottesman, and J. Preskill, ``Quantum accuracy threshold for concatenated distance-3 codes,'' Quant. Inf. Comput. 6, 97\u2013165 (2006), arXiv:quant-ph\/0504218.","DOI":"10.26421\/QIC8.3-4"},{"key":"3","doi-asserted-by":"publisher","unstructured":"J. Haah, M. B. Hastings, D. Poulin, and D. Wecker, ``Magic state distillation with low space overhead and optimal asymptotic input count,'' Quantum 1, 31 (2017), arXiv:1703.07847v1.","DOI":"10.22331\/q-2017-10-03-31"},{"key":"4","doi-asserted-by":"publisher","unstructured":"E. T. Campbell and M. Howard, ``Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost,'' Phys. 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Noh, ``Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits,'' npj Quantum Information 6, 91 (2020), arXiv:2003.03049.","DOI":"10.1038\/s41534-020-00319-5"},{"key":"13","unstructured":"A. G. Fowler and C. Gidney, ``Low overhead quantum computation using lattice surgery,'' arXiv:1808.06709."},{"key":"14","doi-asserted-by":"publisher","unstructured":"T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, et al., ``Scalable designs for quasiparticle-poisoning-protected topological quantum computation with majorana zero modes,'' Phys. Rev. B 95, 235305 (2017), arXiv:1610.05289.","DOI":"10.1103\/PhysRevB.95.235305"},{"key":"15","unstructured":"N. Delfosse, B. Reichardt, and K. Svore, ``Fault-tolerant cat state preparation with low classical and quantum hardware requirement,'' (2020)."},{"key":"16","doi-asserted-by":"publisher","unstructured":"C. Jones, ``Multilevel distillation of magic states for quantum computing,'' Phys. Rev. A 87, 042305 (2013b), arXiv:1210.3388v2.","DOI":"10.1103\/PhysRevA.87.042305"},{"key":"17","doi-asserted-by":"publisher","unstructured":"J. Haah, ``Towers of generalized divisible quantum codes,'' Phys. Rev. A 97, 042327 (2018), arXiv:1709.08658.","DOI":"10.1103\/PhysRevA.97.042327"},{"key":"18","doi-asserted-by":"publisher","unstructured":"S. Bravyi and A. Kitaev, ``Universal quantum computation with ideal Clifford gates and noisy ancillas,'' Phys. Rev. A 71, 022316 (2005), arXiv:quant-ph\/0403025.","DOI":"10.1103\/PhysRevA.71.022316"},{"key":"19","doi-asserted-by":"publisher","unstructured":"J. Haah and M. B. Hastings, ``Codes and protocols for distilling $T$, controlled-$S$, and Toffoli gates,'' Quantum 2, 71 (2018), arXiv:1709.02832.","DOI":"10.22331\/q-2018-06-07-71"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2021-01-20-383\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,1,20]],"date-time":"2021-01-20T17:24:49Z","timestamp":1611163489000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2021-01-20-383\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,20]]},"references-count":20,"URL":"https:\/\/doi.org\/10.22331\/q-2021-01-20-383","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,20]]},"article-number":"383"}}