{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T06:30:52Z","timestamp":1778135452043,"version":"3.51.4"},"reference-count":40,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,11,30]],"date-time":"2023-11-30T00:00:00Z","timestamp":1701302400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"President Scholarship Program at Bar-Ilan University","award":["TAR\/2022\/000657"],"award-info":[{"award-number":["TAR\/2022\/000657"]}]},{"name":"President Scholarship Program at Bar-Ilan University","award":["73795"],"award-info":[{"award-number":["73795"]}]},{"name":"Science and Engineering Research Board (SERB)","award":["TAR\/2022\/000657"],"award-info":[{"award-number":["TAR\/2022\/000657"]}]},{"name":"Science and Engineering Research Board (SERB)","award":["73795"],"award-info":[{"award-number":["73795"]}]},{"name":"Israeli Innovation Authority","award":["TAR\/2022\/000657"],"award-info":[{"award-number":["TAR\/2022\/000657"]}]},{"name":"Israeli Innovation Authority","award":["73795"],"award-info":[{"award-number":["73795"]}]},{"name":"Pazy Foundation","award":["TAR\/2022\/000657"],"award-info":[{"award-number":["TAR\/2022\/000657"]}]},{"name":"Pazy Foundation","award":["73795"],"award-info":[{"award-number":["73795"]}]},{"name":"Israeli Ministry of Science and Technology","award":["TAR\/2022\/000657"],"award-info":[{"award-number":["TAR\/2022\/000657"]}]},{"name":"Israeli Ministry of Science and Technology","award":["73795"],"award-info":[{"award-number":["73795"]}]},{"name":"Quantum Science and Technology Program of the Israeli Council of Higher Education","award":["TAR\/2022\/000657"],"award-info":[{"award-number":["TAR\/2022\/000657"]}]},{"name":"Quantum Science and Technology Program of the Israeli Council of Higher Education","award":["73795"],"award-info":[{"award-number":["73795"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a recurrence formula for the coefficients of the wave function of a quantum walker on an undirected graph with a finite number of nodes. By extending this formula to include extra layers, we develop a simulation model to describe the time evolution of the quantum walker on a multilayer network. The time-averaged probability and the return probability of the quantum walker are studied with Fourier, and Grover walks on multilayer networks. Furthermore, we analyze the impact of decoherence on quantum transport, shedding light on how environmental interactions may impact the behavior of quantum walkers on multilayer network structures.<\/jats:p>","DOI":"10.3390\/e25121610","type":"journal-article","created":{"date-parts":[[2023,11,30]],"date-time":"2023-11-30T09:39:12Z","timestamp":1701337152000},"page":"1610","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Discrete-Time Quantum Walk on Multilayer Networks"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1486-6097","authenticated-orcid":false,"given":"Mahesh N.","family":"Jayakody","sequence":"first","affiliation":[{"name":"Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0606-6900","authenticated-orcid":false,"given":"Priodyuti","family":"Pradhan","sequence":"additional","affiliation":[{"name":"networks.ai Lab, Department of Computer Science and Engineering, Indian Institute of Information Technology Raichur, Raichur 584135, Karnataka, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4722-9844","authenticated-orcid":false,"given":"Dana","family":"Ben Porath","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6198-0725","authenticated-orcid":false,"given":"Eliahu","family":"Cohen","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1126\/science.1229957","article-title":"Universal computation by multiparticle quantum walk","volume":"339","author":"Childs","year":"2013","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1080\/00107151031000110776","article-title":"Quantum random walks: An introductory overview","volume":"44","author":"Kempe","year":"2003","journal-title":"Contemp. 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