{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:44:23Z","timestamp":1760031863306,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,6]],"date-time":"2025-04-06T00:00:00Z","timestamp":1743897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation","award":["DMS-1439786","507536"],"award-info":[{"award-number":["DMS-1439786","507536"]}]},{"name":"Simons Foundation Institute","award":["DMS-1439786","507536"],"award-info":[{"award-number":["DMS-1439786","507536"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper presents a quantum method to tackle optimization challenges. Departing from the typical applications of quantum theory in particle physics, we demonstrate our approach using the elastica problem as a concrete example. The elastica, a classic variational problem extensively studied by mathematicians, serves as an ideal test case. Within quantum theory, our central innovation lies in the way we handle boundary conditions by combining forward and backward propagating wave solutions, a concept inspired by the superposition of forward and backward time-traveling particle waves in quantum mechanics. This approach not only provides a novel solution method for the elastica problem but also opens new pathways for applying quantum mathematical techniques to classical optimization challenges in other domains.<\/jats:p>","DOI":"10.3390\/e27040388","type":"journal-article","created":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T11:24:39Z","timestamp":1744025079000},"page":"388","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantum Elastica"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2138-3517","authenticated-orcid":false,"given":"Davi","family":"Geiger","sequence":"first","affiliation":[{"name":"Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0665-967X","authenticated-orcid":false,"given":"Michael","family":"Werman","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, The Hebrew University, Jerusalem 9190401, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1103\/RevModPhys.21.425","article-title":"Classical Electrodynamics in Terms of Direct Interparticle Action","volume":"21","author":"Wheeler","year":"1949","journal-title":"Rev. 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