{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:34:52Z","timestamp":1760240092809,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,3,9]],"date-time":"2019-03-09T00:00:00Z","timestamp":1552089600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["PINV15-208"],"award-info":[{"award-number":["PINV15-208"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work we show how to use a quantum adiabatic algorithm to solve multiobjective optimization problems. For the first time, we demonstrate a theorem proving that the quantum adiabatic algorithm can find Pareto-optimal solutions in finite-time, provided some restrictions to the problem are met. A numerical example illustrates an application of the theorem to a well-known problem in multiobjective optimization. This result opens the door to solve multiobjective optimization problems using current technology based on quantum annealing.<\/jats:p>","DOI":"10.3390\/axioms8010032","type":"journal-article","created":{"date-parts":[[2019,3,12]],"date-time":"2019-03-12T03:49:31Z","timestamp":1552362571000},"page":"32","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Quantum Adiabatic Algorithm for Multiobjective Combinatorial Optimization"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2855-7201","authenticated-orcid":false,"given":"Benjam\u00edn","family":"Bar\u00e1n","sequence":"first","affiliation":[{"name":"N\u00facleo de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Universidad Nacional de Asunci\u00f3n, San Lorenzo C.P. 2619, Paraguay"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6081-9099","authenticated-orcid":false,"given":"Marcos","family":"Villagra","sequence":"additional","affiliation":[{"name":"N\u00facleo de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Universidad Nacional de Asunci\u00f3n, San Lorenzo C.P. 2619, Paraguay"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,9]]},"reference":[{"unstructured":"Catherine, C., and McGeoch, C.C. (2014). Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice, Morgan and Claypool.","key":"ref_1"},{"unstructured":"Farhi, E., Goldstone, J., Gutman, S., and Sipser, M. (arXiv, 2000). Quantum computation by adiabatic evolution, arXiv.","key":"ref_2"},{"key":"ref_3","first-page":"707","article-title":"A survey on multi-objective evolutionary algorithms for many-objective problems","volume":"58","author":"Brizuela","year":"2014","journal-title":"Comput. Optim. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1080\/00107514.2018.1450720","article-title":"A cross-disciplinary introduction to quantum annealing-based algorithms","volume":"59","author":"McGeoch","year":"2018","journal-title":"Contemp. Phys."},{"doi-asserted-by":"crossref","unstructured":"Grover, L. (1996, January 22\u201324). A fast quantum mechanical algorithm for database search. Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (STOC), Philadelphia, PA, USA.","key":"ref_5","DOI":"10.1145\/237814.237866"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"11701184","DOI":"10.1137\/040605072","article-title":"Grover\u2019s quantum algorithm applied to global optimization","volume":"15","author":"Baritompa","year":"2005","journal-title":"SIAM J. Optim."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1109\/ACCESS.2014.2327596","article-title":"Quantum-Assisted Routing Optimization for Self-Organizing Networks","volume":"2","author":"Alanis","year":"2014","journal-title":"IEEE Access"},{"doi-asserted-by":"crossref","unstructured":"Fogel, G., Bar\u00e1n, B., and Villagra, M. (2017, January 3\u20136). Comparison of two types of Quantum Oracles based on Grover\u2019s Adaptative Search Algorithm for Multiobjective Optimization Problems. Proceedings of the 10th International Workshop on Computational Optimization (WCO), Federated Conference in Computer Science and Information Systems (FedCSIS), ACSIS, Prague, Czech Republic.","key":"ref_8","DOI":"10.15439\/2017F259"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1103\/RevModPhys.80.1061","article-title":"Quantum annealing and quantum computation","volume":"80","author":"Das","year":"2008","journal-title":"Rev. Mod. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.entcs.2016.12.003","article-title":"Multiobjective optimization in a quantum adiabatic computer","volume":"329","author":"Villagra","year":"2016","journal-title":"Electr. Notes Theor. Comput. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1145\/321906.321910","article-title":"On finding the maxima of a set of vectors","volume":"22","author":"Kung","year":"1975","journal-title":"J. ACM"},{"unstructured":"Papadimitriou, C., and Yannakakis, M. (2000, January 12\u201314). On the approximability of trade-offs and optimal access of web sources. Proceedings of the 41st Annual Symposium on Foundations of Computer Science (FOCS), Washington, DC, USA.","key":"ref_12"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/s002910000046","article-title":"A survey and annotated bibliography of multiobjective combinatorial optimization","volume":"22","author":"Ehrgott","year":"2000","journal-title":"OR Spektrum"},{"unstructured":"Ambainis, A., and Regev, O. (arXiv, 2004). An elementary proof of the quantum adiabatic theorem, arXiv.","key":"ref_14"},{"doi-asserted-by":"crossref","unstructured":"Wim van Dam, W., Mosca, M., and Vazirani, U. (2001, January 14\u201317). How powerful is adiabatic quantum computation?. Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS), Las Vegas, NV, USA.","key":"ref_15","DOI":"10.1109\/SFCS.2001.959902"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1038\/nature16059","article-title":"Undecidability of the Spectral Gap","volume":"528","author":"Cubitt","year":"2015","journal-title":"Nature"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1038\/nature23474","article-title":"Quantum machine learning","volume":"549","author":"Biamonte","year":"2017","journal-title":"Nature"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/1\/32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:37:39Z","timestamp":1760186259000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/1\/32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,9]]},"references-count":17,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["axioms8010032"],"URL":"https:\/\/doi.org\/10.3390\/axioms8010032","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2019,3,9]]}}}