{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T08:20:22Z","timestamp":1781684422294,"version":"3.54.5"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T00:00:00Z","timestamp":1715644800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T00:00:00Z","timestamp":1715644800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a new method to implement joint measurements using a 4-qubit twist defect on a rotated surface code. The proposed method enables us to perform logical<jats:italic>S<\/jats:italic>(Phase gate),<jats:italic>T<\/jats:italic>(<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\pi \/8$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>\u03c0<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mn>8<\/mml:mn><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>gate), and<jats:italic>H<\/jats:italic>(Hadamard) with low overhead. Combined with other universal quantum gates, we can implement fault-tolerant quantum computation at the lattice surgery level beyond the gate level while saving considerable resources. We compare our method with previous methods using benchmark circuits by calculating the space and time costs. The proposed method requires additional lines of physical qubits for each encoded patch. Although it slightly increases the space cost for logical<jats:italic>H<\/jats:italic>compared to the previous work, it reduces the time cost. In addition, the proposed method decreases the space cost and time cost by introducing a 4-qubit twist defect for logical<jats:italic>S<\/jats:italic>and<jats:italic>T<\/jats:italic>. Therefore, the overall space-time cost is reduced.<\/jats:p>","DOI":"10.1007\/s11128-024-04389-8","type":"journal-article","created":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T06:01:56Z","timestamp":1715666516000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fault-tolerant quantum computation using low-cost joint measurements"],"prefix":"10.1007","volume":"23","author":[{"given":"Yujin","family":"Kang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonghyun","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinyoung","family":"Ha","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Heo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,5,14]]},"reference":[{"key":"4389_CR1","doi-asserted-by":"crossref","unstructured":"Shor, P.W.: Fault-tolerant quantum computation. In: Proceedings of 37th Conference on Foundations of Computer Science, pp. 56\u201365 (1996). IEEE","DOI":"10.1109\/SFCS.1996.548464"},{"key":"4389_CR2","doi-asserted-by":"crossref","unstructured":"Preskill, J.: Reliable quantum computers. Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 454(1969), 385\u2013410 (1998)","DOI":"10.1098\/rspa.1998.0167"},{"key":"4389_CR3","unstructured":"Gottesman, D.: Opportunities and challenges in fault-tolerant quantum computation. arXiv preprint arXiv:2210.15844 (2022)"},{"issue":"2","key":"4389_CR4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.83.020302","volume":"83","author":"DS Wang","year":"2011","unstructured":"Wang, D.S., Fowler, A.G., Hollenberg, L.C.: Surface code quantum computing with error rates over 1%. Phys. Rev. A 83(2), 020302 (2011)","journal-title":"Phys. Rev. A"},{"key":"4389_CR5","doi-asserted-by":"publisher","first-page":"392","DOI":"10.22331\/q-2021-02-04-392","volume":"5","author":"JE Bourassa","year":"2021","unstructured":"Bourassa, J.E., Alexander, R.N., Vasmer, M., Patil, A., Tzitrin, I., Matsuura, T., Su, D., Baragiola, B.Q., Guha, S., Dauphinais, G.: Blueprint for a scalable photonic fault-tolerant quantum computer. Quantum 5, 392 (2021)","journal-title":"Quantum"},{"issue":"1","key":"4389_CR6","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/S0003-4916(02)00018-0","volume":"303","author":"AY Kitaev","year":"2003","unstructured":"Kitaev, A.Y.: Fault-tolerant quantum computation by anyons. Ann. Phys. 303(1), 2\u201330 (2003)","journal-title":"Ann. Phys."},{"issue":"19","key":"4389_CR7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.98.190504","volume":"98","author":"R Raussendorf","year":"2007","unstructured":"Raussendorf, R., Harrington, J.: Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98(19), 190504 (2007)","journal-title":"Phys. Rev. Lett."},{"issue":"7911","key":"4389_CR8","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1038\/s41586-022-04566-8","volume":"605","author":"S Krinner","year":"2022","unstructured":"Krinner, S., Lacroix, N., Remm, A., Di Paolo, A., Genois, E., Leroux, C., Hellings, C., Lazar, S., Swiadek, F., Herrmann, J.: Realizing repeated quantum error correction in a distance-three surface code. Nature 605(7911), 669\u2013674 (2022)","journal-title":"Nature"},{"key":"4389_CR9","doi-asserted-by":"crossref","unstructured":"Bravyi, S., Englbrecht, M., K\u00f6nig, R., Peard, N.: Correcting coherent errors with surface codes. npj Quantum Inf. 4(1), 55 (2018)","DOI":"10.1038\/s41534-018-0106-y"},{"issue":"6","key":"4389_CR10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.90.062320","volume":"90","author":"Y Tomita","year":"2014","unstructured":"Tomita, Y., Svore, K.M.: Low-distance surface codes under realistic quantum noise. Phys. Rev. A 90(6), 062320 (2014)","journal-title":"Phys. Rev. A"},{"key":"4389_CR11","doi-asserted-by":"crossref","unstructured":"Nielsen, M.A., Chuang, I.: Quantum computation and quantum information. American Association of Physics Teachers (2002)","DOI":"10.1119\/1.1463744"},{"issue":"3","key":"4389_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.86.032324","volume":"86","author":"AG Fowler","year":"2012","unstructured":"Fowler, A.G., Mariantoni, M., Martinis, J.M., Cleland, A.N.: Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86(3), 032324 (2012)","journal-title":"Phys. Rev. A"},{"key":"4389_CR13","doi-asserted-by":"publisher","first-page":"62","DOI":"10.22331\/q-2018-05-04-62","volume":"2","author":"D Litinski","year":"2018","unstructured":"Litinski, D., Oppen, F.: Lattice surgery with a twist: simplifying Clifford gates of surface codes. Quantum 2, 62 (2018)","journal-title":"Quantum"},{"issue":"12","key":"4389_CR14","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/14\/12\/123011","volume":"14","author":"C Horsman","year":"2012","unstructured":"Horsman, C., Fowler, A.G., Devitt, S., Van Meter, R.: Surface code quantum computing by lattice surgery. New J. Phys. 14(12), 123011 (2012)","journal-title":"New J. Phys."},{"key":"4389_CR15","unstructured":"Fowler, A.G., Gidney, C.: Low overhead quantum computation using lattice surgery. arXiv preprint arXiv:1808.06709 (2018)"},{"issue":"6","key":"4389_CR16","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s11128-022-03556-z","volume":"21","author":"J Lee","year":"2022","unstructured":"Lee, J., Kang, Y., Ha, J., Heo, J.: Lattice surgery-based surface code architecture using remote logical cnot operation. Quantum Inf. Process. 21(6), 217 (2022)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"4389_CR17","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/aadd1a","volume":"4","author":"L Lao","year":"2018","unstructured":"Lao, L., Wee, B., Ashraf, I., Someren, J., Khammassi, N., Bertels, K., Almudever, C.G.: Mapping of lattice surgery-based quantum circuits on surface code architectures. Quantum Sci. Technol. 4(1), 015005 (2018)","journal-title":"Quantum Sci. Technol."},{"issue":"2","key":"4389_CR18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.71.022316","volume":"71","author":"S Bravyi","year":"2005","unstructured":"Bravyi, S., Kitaev, A.: Universal quantum computation with ideal Clifford gates and noisy ancillas. Phys. Rev. A 71(2), 022316 (2005)","journal-title":"Phys. Rev. A"},{"key":"4389_CR19","doi-asserted-by":"publisher","first-page":"383","DOI":"10.22331\/q-2021-01-20-383","volume":"5","author":"J Haah","year":"2021","unstructured":"Haah, J., Hastings, M.B.: Measurement sequences for magic state distillation. Quantum 5, 383 (2021)","journal-title":"Quantum"},{"key":"4389_CR20","doi-asserted-by":"publisher","first-page":"128","DOI":"10.22331\/q-2019-03-05-128","volume":"3","author":"D Litinski","year":"2019","unstructured":"Litinski, D.: A game of surface codes: large-scale quantum computing with lattice surgery. Quantum 3, 128 (2019)","journal-title":"Quantum"},{"issue":"5","key":"4389_CR21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.62.052316","volume":"62","author":"X Zhou","year":"2000","unstructured":"Zhou, X., Leung, D.W., Chuang, I.L.: Methodology for quantum logic gate construction. Phys. Rev. A 62(5), 052316 (2000)","journal-title":"Phys. Rev. A"},{"key":"4389_CR22","unstructured":"Beverland, M.E., Huang, S., Kliuchnikov, V.: Fault tolerance of stabilizer channels. arXiv preprint arXiv:2401.12017 (2024)"},{"issue":"7841","key":"4389_CR23","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1038\/s41586-020-03079-6","volume":"589","author":"A Erhard","year":"2021","unstructured":"Erhard, A., Poulsen Nautrup, H., Meth, M., Postler, L., Stricker, R., Stadler, M., Negnevitsky, V., Ringbauer, M., Schindler, P., Briegel, H.J.: Entangling logical qubits with lattice surgery. Nature 589(7841), 220\u2013224 (2021)","journal-title":"Nature"},{"key":"4389_CR24","doi-asserted-by":"crossref","unstructured":"Riesebos, L., Fu, X., Varsamopoulos, S., Almudever, C.G., Bertels, K.: Pauli frames for quantum computer architectures. In: Proceedings of the 54th Annual Design Automation Conference 2017, pp. 1\u20136 (2017)","DOI":"10.1145\/3061639.3062300"},{"issue":"1","key":"4389_CR25","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.3.010331","volume":"3","author":"C Chamberland","year":"2022","unstructured":"Chamberland, C., Campbell, E.T.: Universal quantum computing with twist-free and temporally encoded lattice surgery. PRX Quantum 3(1), 010331 (2022)","journal-title":"PRX Quantum"},{"issue":"1","key":"4389_CR26","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/aa5709","volume":"19","author":"D Herr","year":"2017","unstructured":"Herr, D., Nori, F., Devitt, S.J.: Lattice surgery translation for quantum computation. New J. Phys. 19(1), 013034 (2017)","journal-title":"New J. Phys."},{"issue":"19","key":"4389_CR27","doi-asserted-by":"publisher","first-page":"1296","DOI":"10.1002\/qua.24856","volume":"115","author":"CJ Trout","year":"2015","unstructured":"Trout, C.J., Brown, K.R.: Magic state distillation and gate compilation in quantum algorithms for quantum chemistry. Int. J. Quantum Chem. 115(19), 1296\u20131304 (2015)","journal-title":"Int. J. Quantum Chem."},{"issue":"5","key":"4389_CR28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.86.052329","volume":"86","author":"S Bravyi","year":"2012","unstructured":"Bravyi, S., Haah, J.: Magic-state distillation with low overhead. Phys. Rev. A 86(5), 052329 (2012)","journal-title":"Phys. Rev. A"},{"key":"4389_CR29","doi-asserted-by":"publisher","first-page":"71","DOI":"10.22331\/q-2018-06-07-71","volume":"2","author":"J Haah","year":"2018","unstructured":"Haah, J., Hastings, M.B.: Codes and protocols for distilling $$ t $$, controlled-$$ s $$, and Toffoli gates. Quantum 2, 71 (2018)","journal-title":"Quantum"},{"issue":"2","key":"4389_CR30","volume":"6","author":"S Bravyi","year":"2016","unstructured":"Bravyi, S., Smith, G., Smolin, J.A.: Trading classical and quantum computational resources. Phys. Rev. X 6(2), 021043 (2016)","journal-title":"Phys. Rev. X"},{"key":"4389_CR31","unstructured":"Adedoyin, A., Ambrosiano, J., Anisimov, P., Casper, W., Chennupati, G., Coffrin, C., Djidjev, H., Gunter, D., Karra, S., Lemons, N., et al.: Quantum algorithm implementations for beginners. arXiv preprint arXiv:1804.03719 (2018)"},{"issue":"1","key":"4389_CR32","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1038\/s41534-020-0257-5","volume":"6","author":"Y Nam","year":"2020","unstructured":"Nam, Y., Su, Y., Maslov, D.: Approximate quantum Fourier transform with o (n log (n)) t gates. NPJ Quantum Inf. 6(1), 26 (2020)","journal-title":"NPJ Quantum Inf."},{"key":"4389_CR33","doi-asserted-by":"crossref","unstructured":"Garc\u00eda-Mart\u00edn, D., Sierra, G.: Five experimental tests on the 5-qubit ibm quantum computer. arXiv preprint arXiv:1712.05642 (2017)","DOI":"10.4236\/jamp.2018.67123"},{"issue":"1","key":"4389_CR34","first-page":"1","volume":"11","author":"C-C Lin","year":"2014","unstructured":"Lin, C.-C., Chakrabarti, A., Jha, N.K.: Qlib: quantum module library. ACM J. Emerg. Technol. Comput. Syst. 11(1), 1\u201320 (2014)","journal-title":"ACM J. Emerg. Technol. Comput. Syst."},{"key":"4389_CR35","doi-asserted-by":"publisher","first-page":"2","DOI":"10.22331\/q-2017-04-25-2","volume":"1","author":"TJ Yoder","year":"2017","unstructured":"Yoder, T.J., Kim, I.H.: The surface code with a twist. Quantum 1, 2 (2017)","journal-title":"Quantum"},{"key":"4389_CR36","unstructured":"Landahl, A.J., Ryan-Anderson, C.: Quantum computing by color-code lattice surgery. arXiv preprint arXiv:1407.5103 (2014)"},{"issue":"3","key":"4389_CR37","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/ab0199","volume":"21","author":"C Vuillot","year":"2019","unstructured":"Vuillot, C., Lao, L., Criger, B., Almud\u00e9ver, C.G., Bertels, K., Terhal, B.M.: Code deformation and lattice surgery are gauge fixing. New J. Phys. 21(3), 033028 (2019)","journal-title":"New J. Phys."},{"issue":"7994","key":"4389_CR38","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1038\/s41586-023-06846-3","volume":"625","author":"RS Gupta","year":"2024","unstructured":"Gupta, R.S., Sundaresan, N., Alexander, T., Wood, C.J., Merkel, S.T., Healy, M.B., Hillenbrand, M., Jochym-O\u2019Connor, T., Wootton, J.R., Yoder, T.J.: Encoding a magic state with beyond break-even fidelity. Nature 625(7994), 259\u2013263 (2024)","journal-title":"Nature"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04389-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-024-04389-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04389-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,18]],"date-time":"2024-11-18T22:54:19Z","timestamp":1731970459000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-024-04389-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,14]]},"references-count":38,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["4389"],"URL":"https:\/\/doi.org\/10.1007\/s11128-024-04389-8","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,14]]},"assertion":[{"value":"1 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 April 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 May 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"190"}}