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However, demonstrations of the usefulness of such NISQ devices are still rare. In this work, we consider a practical railway dispatching problem: delay and conflict management on single-track railway lines. We examine the train dispatching consequences of the arrival of an already delayed train to a given network segment. This problem is computationally hard and needs to be solved almost in real time. We introduce a quadratic unconstrained binary optimization (QUBO) model of this problem, which is compatible with the emerging quantum annealing technology. The model\u2019s instances can be executed on present-day quantum annealers. As a proof-of-concept, we solve selected real-life problems from the Polish railway network using D-Wave quantum annealers. As a reference, we also provide solutions calculated with classical methods, including the conventional solution of a linear integer version of the model as well as the solution of the QUBO model using a tensor network-based algorithm. Our preliminary results illustrate the degree of difficulty of real-life railway instances for the current quantum annealing technology. Moreover, our analysis shows that the new generation of quantum annealers (the advantage system) does not perform well on those instances, either.<\/jats:p>","DOI":"10.3390\/e25020191","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T02:51:37Z","timestamp":1674096697000},"page":"191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Quantum Annealing in the NISQ Era: Railway Conflict Management"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7386-5441","authenticated-orcid":false,"given":"Krzysztof","family":"Domino","sequence":"first","affiliation":[{"name":"Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Ba\u0142tycka 5, 44-100 Gliwice, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2710-493X","authenticated-orcid":false,"given":"M\u00e1ty\u00e1s","family":"Koniorczyk","sequence":"additional","affiliation":[{"name":"Wigner Research Centre, Konkoly-Thege M. \u00fat 29-33, H-1525 Budapest, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7447-3447","authenticated-orcid":false,"given":"Krzysztof","family":"Krawiec","sequence":"additional","affiliation":[{"name":"Faculty of Transport and Aviation Engineering, Silesian University of Technology, 40-019 Katowice, Poland"}]},{"given":"Konrad","family":"Ja\u0142owiecki","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Silesia, 41-500 Chorz\u00f3w, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0504-6932","authenticated-orcid":false,"given":"Sebastian","family":"Deffner","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA"},{"name":"Instituto de F\u00edsica \u2018Gleb Wataghin\u2019, Universidade Estadual de Campinas, Campinas 13083-859, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1454-1591","authenticated-orcid":false,"given":"Bart\u0142omiej","family":"Gardas","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Ba\u0142tycka 5, 44-100 Gliwice, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"020504","DOI":"10.1088\/2058-9565\/ab0441","article-title":"The US National Quantum Initiative","volume":"4","author":"Raymer","year":"2019","journal-title":"Quantum Sci. 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