{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T01:24:37Z","timestamp":1776216277750,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:00:00Z","timestamp":1604188800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:00:00Z","timestamp":1604188800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003593","name":"CNPq","doi-asserted-by":"crossref","award":["0000"],"award-info":[{"award-number":["0000"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"crossref"}]},{"name":"CAPES Brasil","award":["0000"],"award-info":[{"award-number":["0000"]}]},{"DOI":"10.13039\/501100004586","name":"FAPERJ","doi-asserted-by":"crossref","award":["0000"],"award-info":[{"award-number":["0000"]}],"id":[{"id":"10.13039\/501100004586","id-type":"DOI","asserted-by":"crossref"}]},{"name":"FAPERJ JCNE","award":["000"],"award-info":[{"award-number":["000"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2020,11]]},"DOI":"10.1007\/s11128-020-02917-w","type":"journal-article","created":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T08:03:07Z","timestamp":1605254587000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the equivalence between quantum and random walks on finite graphs"],"prefix":"10.1007","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9968-0194","authenticated-orcid":false,"given":"Matheus G.","family":"Andrade","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9712-1930","authenticated-orcid":false,"given":"Franklin","family":"de Lima\u00a0Marquezino","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9341-6619","authenticated-orcid":false,"given":"Daniel R.","family":"Figueiredo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,11,13]]},"reference":[{"key":"2917_CR1","doi-asserted-by":"crossref","unstructured":"Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.: Quantum walks on graphs. In: Proceedings of the 33rd annual ACM symposium on theory of computing, pp. 50\u201359. ACM, (2001)","DOI":"10.1145\/380752.380758"},{"issue":"2","key":"2917_CR2","doi-asserted-by":"publisher","first-page":"1687","DOI":"10.1103\/PhysRevA.48.1687","volume":"48","author":"Y Aharonov","year":"1993","unstructured":"Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48(2), 1687 (1993)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"2917_CR3","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1137\/S0097539705447311","volume":"37","author":"A Ambainis","year":"2007","unstructured":"Ambainis, A.: Quantum walk algorithm for element distinctness. SIAM J. Comput. 37(1), 210\u2013239 (2007)","journal-title":"SIAM J. Comput."},{"key":"2917_CR4","doi-asserted-by":"crossref","unstructured":"Berry, D.W., Childs, A.M., Kothari, R.: Hamiltonian simulation with nearly optimal dependence on all parameters. In: 2015 IEEE 56th annual symposium on foundations of computer science, pp. 792\u2013809. IEEE, (2015)","DOI":"10.1109\/FOCS.2015.54"},{"issue":"5","key":"2917_CR5","doi-asserted-by":"publisher","first-page":"052330","DOI":"10.1103\/PhysRevA.91.052330","volume":"91","author":"S Boettcher","year":"2015","unstructured":"Boettcher, S., Falkner, S., Portugal, R.: Relation between random walks and quantum walks. Phys. Rev. A 91(5), 052330 (2015)","journal-title":"Phys. Rev. A"},{"issue":"18","key":"2917_CR6","doi-asserted-by":"publisher","first-page":"180501","DOI":"10.1103\/PhysRevLett.102.180501","volume":"102","author":"AM Childs","year":"2009","unstructured":"Childs, A.M.: Universal computation by quantum walk. Phys. Rev. Lett. 102(18), 180501 (2009)","journal-title":"Phys. Rev. Lett."},{"issue":"6121","key":"2917_CR7","doi-asserted-by":"publisher","first-page":"791","DOI":"10.1126\/science.1229957","volume":"339","author":"AM Childs","year":"2013","unstructured":"Childs, A.M., Gosset, D., Webb, Z.: Universal computation by multiparticle quantum walk. Science 339(6121), 791\u2013794 (2013)","journal-title":"Science"},{"key":"2917_CR8","volume-title":"Quantum Mechanics and Path Integrals","author":"RP Feynman","year":"2010","unstructured":"Feynman, R.P., Hibbs, A.R., Styer, D.F.: Quantum Mechanics and Path Integrals. Courier Corporation, North Chelmsford (2010)"},{"key":"2917_CR9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511613586","volume-title":"Finite Markov Chains and Algorithmic Applications","author":"O H\u00e4ggstr\u00f6m","year":"2002","unstructured":"H\u00e4ggstr\u00f6m, O., et al.: Finite Markov Chains and Algorithmic Applications, vol. 52. Cambridge University Press, Cambridge (2002)"},{"issue":"1","key":"2917_CR10","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","volume":"57","author":"WK Hastings","year":"1970","unstructured":"Hastings, W.K.: Monte carlo sampling methods using markov chains and their applications. Biometrika 57(1), 97\u2013109 (1970)","journal-title":"Biometrika"},{"issue":"1","key":"2917_CR11","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1080\/00107510902734722","volume":"50","author":"J Kempe","year":"2009","unstructured":"Kempe, J.: Quantum random walks: an introductory overview. Contemp. Phys. 50(1), 339\u2013359 (2009)","journal-title":"Contemp. Phys."},{"issue":"4598","key":"2917_CR12","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S Kirkpatrick","year":"1983","unstructured":"Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671\u2013680 (1983)","journal-title":"Science"},{"issue":"4","key":"2917_CR13","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1007\/s11128-017-1807-4","volume":"17","author":"N Konno","year":"2018","unstructured":"Konno, N., Portugal, R., Sato, I., Segawa, E.: Partition-based discrete-time quantum walks. Quantum Inf. Process. 17(4), 100 (2018)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"2917_CR14","first-page":"1","volume":"2","author":"L Lov\u00e1sz","year":"1993","unstructured":"Lov\u00e1sz, L., et al.: Random walks on graphs: a survey. Comb. Paul Erdos Eighty 2(1), 1\u201346 (1993)","journal-title":"Comb. Paul Erdos Eighty"},{"issue":"4","key":"2917_CR15","doi-asserted-by":"publisher","first-page":"042330","DOI":"10.1103\/PhysRevA.81.042330","volume":"81","author":"NB Lovett","year":"2010","unstructured":"Lovett, N.B., Cooper, S., Everitt, M., Trevers, M., Kendon, V.: Universal quantum computation using the discrete-time quantum walk. Phys. Rev. A 81(4), 042330 (2010)","journal-title":"Phys. Rev. A"},{"key":"2917_CR16","first-page":"08","volume":"40","author":"F Magniez","year":"2006","unstructured":"Magniez, F., Nayak, A., Roland, J., Santha, M.: Search via quantum walk. SIAM J. Comput. 40, 08 (2006)","journal-title":"SIAM J. Comput."},{"issue":"3","key":"2917_CR17","doi-asserted-by":"publisher","first-page":"839","DOI":"10.1007\/s11128-014-0908-6","volume":"14","author":"M Montero","year":"2015","unstructured":"Montero, M.: Quantum walk with a general coin: exact solution and asymptotic properties. Quantum Inf. Process. 14(3), 839\u2013866 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"2917_CR18","doi-asserted-by":"publisher","first-page":"062326","DOI":"10.1103\/PhysRevA.95.062326","volume":"95","author":"M Montero","year":"2017","unstructured":"Montero, M.: Quantum and random walks as universal generators of probability distributions. Phys. Rev. A 95(6), 062326 (2017)","journal-title":"Phys. Rev. A"},{"key":"2917_CR19","unstructured":"Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: Bringing order to the web. Technical report, Stanford InfoLab, (1999)"},{"key":"2917_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6336-8","volume-title":"Quantum walks and search algorithms","author":"R Portugal","year":"2013","unstructured":"Portugal, R.: Quantum walks and search algorithms. Springer, Berlin (2013)"},{"key":"2917_CR21","unstructured":"Portugal, R., Segawa, E.: Coined quantum walks as quantum markov chains. arXiv preprint arXiv:1612.02448, (2016)"},{"issue":"1","key":"2917_CR22","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s11128-015-1149-z","volume":"15","author":"R Portugal","year":"2016","unstructured":"Portugal, R., Santos, R.A., Fernandes, T.D., Gon\u00e7alves, D.N.: The staggered quantum walk model. Quantum Inf. Process. 15(1), 85\u2013101 (2016)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"2917_CR23","doi-asserted-by":"publisher","first-page":"013001","DOI":"10.1088\/1367-2630\/13\/1\/013001","volume":"13","author":"PP Rohde","year":"2011","unstructured":"Rohde, P.P., Schreiber, A., \u0160tefa\u0148\u00e1k, M., Jex, I., Silberhorn, C.: Multi-walker discrete time quantum walks on arbitrary graphs, their properties and their photonic implementation. New J. Phys. 13(1), 013001 (2011)","journal-title":"New J. Phys."},{"key":"2917_CR24","doi-asserted-by":"publisher","first-page":"062349","DOI":"10.1103\/PhysRevA.81.062349","volume":"81","author":"A Romanelli","year":"2010","unstructured":"Romanelli, A.: Distribution of chirality in the quantum walk: Markov process and entanglement. Phys. Rev. A 81, 062349 (2010)","journal-title":"Phys. Rev. A"},{"issue":"3\u20134","key":"2917_CR25","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/j.physa.2004.02.061","volume":"338","author":"A Romanelli","year":"2004","unstructured":"Romanelli, A., Schifino, A.S., Siri, R., Abal, G., Auyuanet, A., Donangelo, R.: Quantum random walk on the line as a markovian process. Phys. A Stat. Mech. Its Appl. 338(3\u20134), 395\u2013405 (2004)","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"2917_CR26","doi-asserted-by":"publisher","first-page":"022106","DOI":"10.1103\/PhysRevA.95.022106","volume":"95","author":"I Siloi","year":"2017","unstructured":"Siloi, I., Benedetti, C., Piccinini, E., Piilo, J., Maniscalco, S., Paris, M.G.A., Bordone, P.: Noisy quantum walks of two indistinguishable interacting particles. Phys. Rev. A 95, 022106 (2017)","journal-title":"Phys. Rev. A"},{"issue":"48","key":"2917_CR27","doi-asserted-by":"publisher","first-page":"14965","DOI":"10.1088\/0305-4470\/39\/48\/009","volume":"39","author":"M \u0160tefan\u00e1k","year":"2006","unstructured":"\u0160tefan\u00e1k, M., Kiss, T., Jex, I., Mohring, B.: The meeting problem in the quantum walk. J. Phys. A Math. Gen. 39(48), 14965 (2006)","journal-title":"J. Phys. A Math. Gen."},{"key":"2917_CR28","unstructured":"Szegedy, M.: Quantum speed-up of markov chain based algorithms. In: 45th annual IEEE symposium on foundations of computer science, pp. 32\u201341, (2004)"},{"issue":"5","key":"2917_CR29","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1007\/s11128-012-0432-5","volume":"11","author":"SE Venegas-Andraca","year":"2012","unstructured":"Venegas-Andraca, S.E.: Quantum walks: a comprehensive review. Quantum Inf. Process. 11(5), 1015\u20131106 (2012)","journal-title":"Quantum Inf. Process."},{"issue":"2","key":"2917_CR30","doi-asserted-by":"publisher","first-page":"022323","DOI":"10.1103\/PhysRevA.81.022323","volume":"81","author":"JD Whitfield","year":"2010","unstructured":"Whitfield, J.D., Rodr\u00edguez-Rosario, C.A., Aspuru-Guzik, A.: Quantum stochastic walks: a generalization of classical random walks and quantum walks. Phys. Rev. A 81(2), 022323 (2010)","journal-title":"Phys. Rev. A"},{"key":"2917_CR31","doi-asserted-by":"publisher","first-page":"022307","DOI":"10.1103\/PhysRevA.85.022307","volume":"85","author":"P Xue","year":"2012","unstructured":"Xue, P., Sanders, B.C.: Two quantum walkers sharing coins. Phys. Rev. A 85, 022307 (2012)","journal-title":"Phys. Rev. A"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02917-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-020-02917-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02917-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T08:55:56Z","timestamp":1606208156000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-020-02917-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11]]},"references-count":31,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["2917"],"URL":"https:\/\/doi.org\/10.1007\/s11128-020-02917-w","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11]]},"assertion":[{"value":"10 February 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 October 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 November 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"417"}}