{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T12:57:40Z","timestamp":1784379460405,"version":"3.55.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,11,12]],"date-time":"2014-11-12T00:00:00Z","timestamp":1415750400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2015,2]]},"DOI":"10.1007\/s11128-014-0867-y","type":"journal-article","created":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T11:08:19Z","timestamp":1415963299000},"page":"447-463","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Depth optimization for topological quantum circuits"],"prefix":"10.1007","volume":"14","author":[{"given":"Mohammad","family":"AlFailakawi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Imtiaz","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laila","family":"AlTerkawi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Suha","family":"Hamdan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2014,11,12]]},"reference":[{"key":"867_CR1","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2002","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2002)"},{"key":"867_CR2","unstructured":"Sarma, S.D., Freedman, M., Nayak, C.: Topological quantum computation. Phys. Today 59(7), 32\u201338 (2006)"},{"key":"867_CR3","doi-asserted-by":"crossref","unstructured":"Fowler, A.G., Goyal, K.: Topological cluster state quantum computing. arXiv:0805.3202 [quant-ph] (2009)","DOI":"10.26421\/QIC9.9-10-1"},{"issue":"8","key":"867_CR4","doi-asserted-by":"crossref","first-page":"083032","DOI":"10.1088\/1367-2630\/11\/8\/083032","volume":"11","author":"SJ Devitt","year":"2009","unstructured":"Devitt, S.J., Fowler, A.G., Stephens, A.M., Greentree, A.D., Hollenberg, L.C.L., Munro, W.J., Nemoto, K.: Architectural design for a topological cluster state quantum computer. New J. Phys. 11(8), 083032 (2009)","journal-title":"New J. Phys."},{"issue":"5","key":"867_CR5","doi-asserted-by":"crossref","first-page":"052312","DOI":"10.1103\/PhysRevA.80.052312","volume":"80","author":"AG Fowler","year":"2009","unstructured":"Fowler, A.G., Stephens, A.M., Groszkowski, P.: High-threshold universal quantum computation on the surface code. Phys. Rev. A 80(5), 052312 (2009). (14 pages)","journal-title":"Phys. Rev. A"},{"key":"867_CR6","doi-asserted-by":"crossref","first-page":"032332","DOI":"10.1103\/PhysRevA.82.032332","volume":"82","author":"DA Herrera-Mart\u00ed","year":"2010","unstructured":"Herrera-Mart\u00ed, D.A., Fowler, A.G., Jennings, D., Rudolph, T.: Photonic implementation for the topological cluster-state quantum computer. Phys. Rev. A 82, 032332 (2010)","journal-title":"Phys. Rev. A"},{"key":"867_CR7","doi-asserted-by":"crossref","unstructured":"Brown, B.J., Son, W., Kraus, C.V., Fazio, R., Vedral, V.: Generating topological order from a two-dimensional cluster state using a duality mapping. New J. Phys. 13(6), 065010 (2011)","DOI":"10.1088\/1367-2630\/13\/6\/065010"},{"key":"867_CR8","unstructured":"Fowler, A.G., Devitt, S.J.: A bridge to lower overhead quantum computation. arXiv preprint arXiv:1209.0510 (2012)"},{"issue":"6","key":"867_CR9","doi-asserted-by":"crossref","first-page":"062318","DOI":"10.1103\/PhysRevA.85.062318","volume":"85","author":"M Ohliger","year":"2012","unstructured":"Ohliger, M., Eisert, J.: Efficient measurement-based quantum computing with continuous-variable systems. Phys. Rev. A 85(6), 062318 (2012)","journal-title":"Phys. Rev. A"},{"key":"867_CR10","doi-asserted-by":"crossref","unstructured":"Paler, A., Devitt, S.J., Nemoto, K., Polian, I.: Synthesis of topological quantum circuits. arXiv preprint arXiv:1302.5182 (2013)","DOI":"10.1145\/2765491.2765524"},{"key":"867_CR11","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1038\/nphys1915","volume":"7","author":"J Alicea","year":"2011","unstructured":"Alicea, J., Oreg, Y., Refael, G., von Oppen, F., Fisher, M.P.A.: Non-Abelian statistics and topological quantum information processing in 1D wire networks. Nat. Phys. 7, 412\u2013417 (2011)","journal-title":"Nat. Phys."},{"key":"867_CR12","first-page":"021018","volume":"4","author":"X-J Liu","year":"2014","unstructured":"Liu, X.-J., Wong, C.L.M., Law, K.T.: Non-abelian majorana doublets in time\u2013reversal\u2013invariant topological superconductors. Phys. Rev. X 4, 021018 (2014)","journal-title":"Phys. Rev. X"},{"key":"867_CR13","doi-asserted-by":"crossref","first-page":"1756","DOI":"10.1038\/ncomms2773","volume":"4","author":"NH Nickerson","year":"2013","unstructured":"Nickerson, N.H., Li, Y., Benjamin, S.C.: Topological quantum computing with a very noisy network and local error rates approaching one percent. Nat. Commun. 4, 1756 (2013)","journal-title":"Nat. Commun."},{"key":"867_CR14","unstructured":"Devitt, S., Nemoto, K.: Programming a topological quantum computer. In: Test Symposium (ATS), 2012 IEEE 21st Asian, pp. 55\u201360. IEEE (2012)"},{"key":"867_CR15","unstructured":"Fowler, A.G.: Time-optimal quantum computation. arXiv preprint arXiv:1210.4626 (2012)"},{"key":"867_CR16","doi-asserted-by":"crossref","first-page":"022306","DOI":"10.1103\/PhysRevA.87.022306","volume":"87","author":"NY Yao","year":"2013","unstructured":"Yao, N.Y., Gong, Z.-X., Laumann, C.R., Bennett, S.D., Duan, L.-M., Lukin, M.D., Jiang, L., Gorshkov, A.V.: Quantum logic between remote quantum registers. Phys. Rev. A 87, 022306 (2013)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"867_CR17","first-page":"031007","volume":"2","author":"NC Jones","year":"2012","unstructured":"Jones, N.C., Van Meter, R., Fowler, A.G., McMahon, P.L., Kim, J., Ladd, T.D., Yamamoto, Y.: Layered architecture for quantum computing. Phys. Rev. X 2(3), 031007 (2012)","journal-title":"Phys. Rev. X"},{"key":"867_CR18","doi-asserted-by":"crossref","unstructured":"Abdessaied, N., Wille, R., Soeken, M., Drechsler, R.: Reducing the depth of quantum circuits using additional circuit lines. In: Proceedings of the 5th International Conference on Reversible Computation, RC\u201913, pp. 221\u2013233. Springer, Berlin (2013)","DOI":"10.1007\/978-3-642-38986-3_18"},{"key":"867_CR19","doi-asserted-by":"crossref","unstructured":"Drechsler, R., Wille, R.: Reversible circuits: recent accomplishments and future challenges for an emerging technology. In: Progress in VLSI Design and Test, pp. 383\u2013392. Springer, Berlin (2012)","DOI":"10.1007\/978-3-642-31494-0_53"},{"key":"867_CR20","doi-asserted-by":"crossref","unstructured":"Kerntopf, P., Perkowski, M., Podlaski, K.: Synthesis of reversible circuits: a view on the state-of-the-art. In: 12th IEEE Conference on Nanotechnology (IEEE-NANO), pp. 1\u20136 (2012)","DOI":"10.1109\/NANO.2012.6322176"},{"key":"867_CR21","doi-asserted-by":"crossref","unstructured":"Saeedi, M., Markov, I.L.: Synthesis and optimization of reversible circuits\u2013a survey. ACM Comput. Surv. 45(2), 21 (2013)","DOI":"10.1145\/2431211.2431220"},{"key":"867_CR22","doi-asserted-by":"crossref","unstructured":"Yamashita, S.: An optimization problem for topological quantum computation. In: IEEE 21st Asian Test Symposium (ATS), pp. 61\u201366. IEEE (2012)","DOI":"10.1109\/ATS.2012.45"},{"issue":"14","key":"867_CR23","doi-asserted-by":"crossref","first-page":"140503","DOI":"10.1103\/PhysRevLett.95.140503","volume":"95","author":"NE Bonesteel","year":"2005","unstructured":"Bonesteel, N.E., Hormozi, L., Zikos, G., Simon, S.H.: Braid topologies for quantum computation. Phys. Rev. Lett. 95(14), 140503 (2005)","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"867_CR24","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1109\/TCAD.2007.911334","volume":"27","author":"D Maslov","year":"2008","unstructured":"Maslov, D., Dueck, G.W., Miller, D.M., Negrevergne, C.: Quantum circuit simplification and level compaction. IEEE Trans. Comput. Aid. Des. Integr. Circuits Syst. 27(3), 436\u2013444 (2008)","journal-title":"IEEE Trans. Comput. Aid. Des. Integr. Circuits Syst."},{"issue":"4","key":"867_CR25","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1007\/s11128-012-0482-8","volume":"12","author":"M Arabzadeh","year":"2013","unstructured":"Arabzadeh, M., Saheb Zamani, M., Sedighi, M., Saeedi, M.: Depth-optimized reversible circuit synthesis. Quantum Inf. Process. 12(4), 1677\u20131699 (2013). ISSN 1570\u20130755","journal-title":"Quantum Inf. Process."},{"key":"867_CR26","unstructured":"Bocharov, A., Svore, K.M.: A depth-optimal canonical form for single-qubit quantum circuits. Phys. Rev. Lett. 109, 190501 (2012). arXiv:1206.3223v1"},{"issue":"6","key":"867_CR27","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1109\/TCAD.2013.2244643","volume":"32","author":"M Amy","year":"2013","unstructured":"Amy, M., Maslov, D., Mosca, M., Roetteler, M.: A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits. IEEE Trans. Comput. Aid. Des. Integr. Circuits Syst. 32(6), 818\u2013830 (2013)","journal-title":"IEEE Trans. Comput. Aid. Des. Integr. Circuits Syst."},{"key":"867_CR28","doi-asserted-by":"crossref","unstructured":"Wille, R., Lye, A., Drechsler, R.: Optimal swap gate insertion for nearest neighbor quantum circuits. In: ASP-DAC, pp. 489\u2013494 (2014)","DOI":"10.1109\/ASPDAC.2014.6742939"},{"key":"867_CR29","doi-asserted-by":"crossref","unstructured":"Shafaei, A., Saeedi, M., Pedram, M.: Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures. In: ACM Design Automation Conference (DAC-13), p. 41 (2013)","DOI":"10.1145\/2463209.2488785"},{"issue":"1","key":"867_CR30","first-page":"142","volume":"11","author":"Y Hirata","year":"2011","unstructured":"Hirata, Y., Nakanishi, M., Yamashita, S., Nakashima, Y.: An efficient conversion of quantum circuits to a linear nearest neighbor architecture. Quantum Inf. Comput. 11(1), 142\u2013166 (2011)","journal-title":"Quantum Inf. Comput."},{"issue":"3","key":"867_CR31","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s11128-010-0201-2","volume":"10","author":"M Saeedi","year":"2011","unstructured":"Saeedi, M., Wille, R., Drechsler, R.: Synthesis of quantum circuits for linear nearest neighbor architectures. Quantum Inf. Process. 10(3), 355\u2013377 (2011)","journal-title":"Quantum Inf. Process."},{"key":"867_CR32","doi-asserted-by":"crossref","unstructured":"Matsuo, A., Yamashita, S.: Changing the gate order for optimal lnn conversion. In: Proceedings of the Third International Conference on Reversible Computation, pp. 89\u2013101 (2012)","DOI":"10.1007\/978-3-642-29517-1_8"},{"issue":"10","key":"867_CR33","doi-asserted-by":"crossref","first-page":"3319","DOI":"10.1007\/s11128-013-0601-1","volume":"12","author":"M AlFailakawi","year":"2013","unstructured":"AlFailakawi, M., AlTerkawi, L., Ahmad, I., Hamdan, S.: Line ordering of reversible circuits for linear nearest neighbor realization. Quantum Inf. Process. 12(10), 3319\u20133339 (2013). ISSN 1570\u20130755","journal-title":"Quantum Inf. Process."},{"key":"867_CR34","doi-asserted-by":"crossref","unstructured":"Hashimoto, A., Stevens, J.: Wire routing by optimizing channel assignment within large apertures. In: Proceedings of the 8th Design Automation Workshop, pp. 155\u2013169. ACM (1971)","DOI":"10.1145\/800158.805069"},{"key":"867_CR35","doi-asserted-by":"crossref","unstructured":"Kurdahi, F.J., Parker, A.C.: Real: a program for register allocation. In: Proceedings of the 24th ACM\/IEEE Design Automation Conference, pp. 210\u2013215. ACM (1987)","DOI":"10.1145\/37888.37920"},{"key":"867_CR36","doi-asserted-by":"crossref","unstructured":"Wille, R., Soeken, M., Otterstedt, C., Drechsler, R.: Improving the mapping of reversible circuits to quantum circuits using multiple target lines. In: Design Automation Conference (ASP-DAC), 2013 18th Asia and South Pacific, pp. 145\u2013150. IEEE (2013)","DOI":"10.1109\/ASPDAC.2013.6509587"},{"key":"867_CR37","volume-title":"Genetic Algorithms in Search, Optimization and Machine Learning","author":"DE Goldberg","year":"1989","unstructured":"Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)"},{"issue":"12","key":"867_CR38","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1145\/361604.361619","volume":"17","author":"TL Adam","year":"1974","unstructured":"Adam, T.L., Mani Chandy, K., Dickson, J.R.: A comparison of list schedules for parallel processing systems. Commun. ACM 17(12), 685\u2013690 (1974)","journal-title":"Commun. ACM"},{"key":"867_CR39","doi-asserted-by":"crossref","unstructured":"Wille, R., Grosse, D., Teuber, L., Dueck, G.W., Drechsler, R.: Revlib: An online resource for reversible functions and reversible circuits. In: 38th International Symposium on Multiple Valued Logic (ISMVL), pp. 220\u2013225 (2008)","DOI":"10.1109\/ISMVL.2008.43"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-014-0867-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-014-0867-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-014-0867-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,22]],"date-time":"2022-04-22T05:38:58Z","timestamp":1650605938000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-014-0867-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,12]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["867"],"URL":"https:\/\/doi.org\/10.1007\/s11128-014-0867-y","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,12]]}}}