{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T18:50:05Z","timestamp":1771959005561,"version":"3.50.1"},"reference-count":68,"publisher":"Optica Publishing Group","issue":"19","license":[{"start":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T00:00:00Z","timestamp":1725408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T00:00:00Z","timestamp":1725408000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/100021086","name":"NTT Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100021086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2024,9,9]]},"abstract":"<jats:p>We propose and numerically study the performance of an all-optical machine for tackling combinatorial clustering, one of the unsupervised machine learning problems. A problem instance is encoded into the phase of time-multiplexed optical pulses, which are coupled repulsively through optical delay lines. To maintain uniform pulse amplitudes, we utilize a nonlinear amplifier with gain saturation, enabling our optical architecture to emulate the classical XY-spin system. This solver, called the coherent XY machine, leads to the formation of clusters in an optical phase space and allows us to efficiently identify the solution with post-processing. Additionally, we implement momentum in our solver to provide a powerful mechanism for escaping local minima and searching for the global optimum. Benchmarking our approach with a most advanced Ising-spin-based solver reveals a two-orders-of-magnitude improvement in the time-to-solution of the algorithm. Furthermore, our approach exhibits scaling advantages for larger problems, which will facilitate time- and energy-efficient data clustering.<\/jats:p>","DOI":"10.1364\/oe.526050","type":"journal-article","created":{"date-parts":[[2024,8,20]],"date-time":"2024-08-20T14:00:07Z","timestamp":1724162407000},"page":"33737","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Combinatorial clustering with a coherent XY machine"],"prefix":"10.1364","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6961-6186","authenticated-orcid":true,"given":"Kyungduk","family":"Kim","sequence":"first","affiliation":[{"name":"NTT Research, Inc."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masahito","family":"Kumagai","sequence":"additional","affiliation":[{"name":"NTT Research, Inc."},{"name":"Tohoku University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yoshihisa","family":"Yamamoto","sequence":"additional","affiliation":[{"name":"NTT Research, Inc."},{"name":"Stanford University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"285","published-online":{"date-parts":[[2024,9,4]]},"reference":[{"key":"oe-32-19-33737-R1","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1016\/j.patrec.2009.09.011","volume":"31","author":"Jain","year":"2010","journal-title":"Pattern Recognit. Lett."},{"key":"oe-32-19-33737-R2","doi-asserted-by":"publisher","first-page":"74887","DOI":"10.3389\/fphy.2014.00005","volume":"2","author":"Lucas","year":"2014","journal-title":"Front. Physics"},{"key":"oe-32-19-33737-R3","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s11128-017-1809-2","volume":"17","author":"Kumar","year":"2018","journal-title":"Quantum Inf. Process."},{"key":"oe-32-19-33737-R5","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1007\/s11128-021-03240-8","volume":"20","author":"Arthur","year":"2021","journal-title":"Quantum Inf. Process."},{"key":"oe-32-19-33737-R6","doi-asserted-by":"publisher","first-page":"463","DOI":"10.15803\/ijnc.11.2_463","volume":"11","author":"Kumagai","year":"2021","journal-title":"Int. J. Netw. Comput."},{"key":"oe-32-19-33737-R7","doi-asserted-by":"publisher","first-page":"2669","DOI":"10.1038\/s41598-022-06559-z","volume":"12","author":"Matsumoto","year":"2022","journal-title":"Sci. Rep."},{"key":"oe-32-19-33737-R8","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1038\/s44172-023-00158-0","volume":"3","author":"Inoue","year":"2024","journal-title":"Commun. Eng."},{"key":"oe-32-19-33737-R9","doi-asserted-by":"publisher","first-page":"7248","DOI":"10.1038\/s41467-022-34847-9","volume":"13","author":"Calvanese Strinati","year":"2022","journal-title":"Nat. Commun."},{"key":"oe-32-19-33737-R10","doi-asserted-by":"publisher","first-page":"017301","DOI":"10.1103\/PhysRevLett.132.017301","volume":"132","author":"Strinati","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"oe-32-19-33737-R11","doi-asserted-by":"publisher","author":"Cummins","year":"2024","DOI":"10.48550\/arXiv.2403.16608"},{"key":"oe-32-19-33737-R12","doi-asserted-by":"publisher","first-page":"3251","DOI":"10.1103\/PhysRevLett.76.3251","volume":"76","author":"Blatt","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"oe-32-19-33737-R13","doi-asserted-by":"publisher","first-page":"061101","DOI":"10.1103\/PhysRevE.63.061101","volume":"63","author":"Giada","year":"2001","journal-title":"Phys. Rev. E"},{"key":"oe-32-19-33737-R14","doi-asserted-by":"publisher","first-page":"1661","DOI":"10.1162\/089976604774201631","volume":"16","author":"Quiroga","year":"2004","journal-title":"Neural Comput."},{"key":"oe-32-19-33737-R15","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1103\/PhysRevLett.85.554","volume":"85","author":"Angelini","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"oe-32-19-33737-R16","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1109\/34.908968","volume":"23","author":"Rhouma","year":"2001","journal-title":"IEEE Trans. Pattern Anal. Machine Intell."},{"key":"oe-32-19-33737-R17","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1109\/72.991428","volume":"13","author":"Bohte","year":"2002","journal-title":"IEEE Trans. Neural Netw."},{"key":"oe-32-19-33737-R18","doi-asserted-by":"publisher","first-page":"024102","DOI":"10.1103\/PhysRevLett.98.024102","volume":"98","author":"Miyano","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"oe-32-19-33737-R20","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1134\/S1054661814030146","volume":"24","author":"Novikov","year":"2014","journal-title":"Pattern Recognit. Image Anal."},{"key":"oe-32-19-33737-R21","author":"Kuramoto","year":"1984"},{"key":"oe-32-19-33737-R22","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1038\/s42254-022-00440-8","volume":"4","author":"Mohseni","year":"2022","journal-title":"Nat. Rev. Phys."},{"key":"oe-32-19-33737-R23","doi-asserted-by":"publisher","first-page":"2300055","DOI":"10.1002\/qute.202300055","volume":"6","author":"Stroev","year":"2023","journal-title":"Adv. Quantum Technol."},{"key":"oe-32-19-33737-R24","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1038\/s42254-023-00645-5","volume":"5","author":"McMahon","year":"2023","journal-title":"Nat. Rev. Phys."},{"key":"oe-32-19-33737-R25","doi-asserted-by":"publisher","first-page":"214101","DOI":"10.1103\/PhysRevLett.108.214101","volume":"108","author":"Nixon","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"oe-32-19-33737-R26","doi-asserted-by":"publisher","first-page":"658","DOI":"10.1038\/nphys2372","volume":"8","author":"Hagerstrom","year":"2012","journal-title":"Nat. Phys."},{"key":"oe-32-19-33737-R27","doi-asserted-by":"publisher","first-page":"213902","DOI":"10.1103\/PhysRevLett.122.213902","volume":"122","author":"Pierangeli","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"oe-32-19-33737-R28","doi-asserted-by":"publisher","first-page":"eabh0952","DOI":"10.1126\/sciadv.abh0952","volume":"7","author":"Honjo","year":"2021","journal-title":"Sci. Adv."},{"key":"oe-32-19-33737-R29","first-page":"402","article-title":"Optical clustering for unsupervised learning using coupled microring resonators","volume":"5809","author":"McAulay","year":"2005"},{"key":"oe-32-19-33737-R30","doi-asserted-by":"publisher","author":"Varga","year":"2024","DOI":"10.48550\/arXiv.2405.04142"},{"key":"oe-32-19-33737-R31","doi-asserted-by":"publisher","first-page":"015005","DOI":"10.1088\/2399-6528\/aa9b6b","volume":"2","author":"Sakaguchi","year":"2018","journal-title":"J. Phys. Commun."},{"key":"oe-32-19-33737-R32","doi-asserted-by":"publisher","first-page":"033128","DOI":"10.1063\/1.5127794","volume":"30","author":"Crnki\u0107","year":"2020","journal-title":"Chaos: An Interdiscip. J. Nonlinear Sci."},{"key":"oe-32-19-33737-R33","doi-asserted-by":"publisher","first-page":"064064","DOI":"10.1103\/PhysRevApplied.17.064064","volume":"17","author":"Mallick","year":"2022","journal-title":"Phys. Rev. Appl."},{"key":"oe-32-19-33737-R34","doi-asserted-by":"publisher","first-page":"063853","DOI":"10.1103\/PhysRevA.88.063853","volume":"88","author":"Wang","year":"2013","journal-title":"Phys. Rev. A"},{"key":"oe-32-19-33737-R35","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1038\/nphoton.2014.249","volume":"8","author":"Marandi","year":"2014","journal-title":"Nat. Photonics"},{"key":"oe-32-19-33737-R36","doi-asserted-by":"publisher","first-page":"34089","DOI":"10.1038\/srep34089","volume":"6","author":"Takata","year":"2016","journal-title":"Sci. Rep."},{"key":"oe-32-19-33737-R37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0041-5553(64)90137-5","volume":"4","author":"Polyak","year":"1964","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"oe-32-19-33737-R38","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/S0893-6080(98)00116-6","volume":"12","author":"Qian","year":"1999","journal-title":"Neural Networks"},{"key":"oe-32-19-33737-R39","doi-asserted-by":"publisher","author":"Mourgias-Alexandris","year":"2023","DOI":"10.48550\/arXiv.2304.12594"},{"key":"oe-32-19-33737-R41","doi-asserted-by":"publisher","first-page":"1630014","DOI":"10.1142\/S0217979216300140","volume":"30","author":"Hamerly","year":"2016","journal-title":"Int. J. Mod. Phys. B"},{"key":"oe-32-19-33737-R42","doi-asserted-by":"publisher","first-page":"014004","DOI":"10.1088\/2058-9565\/aa923b","volume":"3","author":"Takeda","year":"2018","journal-title":"Quantum Sci. Technol."},{"key":"oe-32-19-33737-R43","doi-asserted-by":"publisher","first-page":"5787","DOI":"10.1364\/OL.499993","volume":"48","author":"Yonezu","year":"2023","journal-title":"Opt. Lett."},{"key":"oe-32-19-33737-R44","doi-asserted-by":"publisher","first-page":"184102","DOI":"10.1103\/PhysRevLett.110.184102","volume":"110","author":"Nixon","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"oe-32-19-33737-R45","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1038\/s41563-020-0635-6","volume":"19","author":"Parto","year":"2020","journal-title":"Nat. Mater."},{"key":"oe-32-19-33737-R46","doi-asserted-by":"publisher","first-page":"4117","DOI":"10.1515\/nanoph-2020-0137\/pdf","volume":"9","author":"Gershenzon","year":"2020","journal-title":"Nanophotonics"},{"key":"oe-32-19-33737-R47","doi-asserted-by":"publisher","first-page":"043335","DOI":"10.1103\/PhysRevResearch.2.043335","volume":"2","author":"Honari-Latifpour","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"oe-32-19-33737-R48","doi-asserted-by":"publisher","first-page":"033008","DOI":"10.1103\/PhysRevResearch.2.033008","volume":"2","author":"Pal","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"oe-32-19-33737-R49","doi-asserted-by":"publisher","first-page":"125008","DOI":"10.1088\/1367-2630\/aa924b","volume":"19","author":"Lagoudakis","year":"2017","journal-title":"New J. Phys."},{"key":"oe-32-19-33737-R50","doi-asserted-by":"publisher","first-page":"1120","DOI":"10.1038\/nmat4971","volume":"16","author":"Berloff","year":"2017","journal-title":"Nat. Mater."},{"key":"oe-32-19-33737-R51","doi-asserted-by":"publisher","first-page":"4127","DOI":"10.1515\/nanoph-2020-0162","volume":"9","author":"Kalinin","year":"2020","journal-title":"Nanophotonics"},{"key":"oe-32-19-33737-R52","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1038\/s41563-022-01276-4","volume":"21","author":"Tao","year":"2022","journal-title":"Nat. Mater."},{"key":"oe-32-19-33737-R53","doi-asserted-by":"publisher","first-page":"2651","DOI":"10.1515\/nanoph-2023-0818","volume":"13","author":"Peng","year":"2024","journal-title":"Nanophotonics"},{"key":"oe-32-19-33737-R54","doi-asserted-by":"publisher","first-page":"031306","DOI":"10.1063\/5.0187545","volume":"9","author":"Chalupnik","year":"2024","journal-title":"APL Photonics"},{"key":"oe-32-19-33737-R55","doi-asserted-by":"publisher","first-page":"113023","DOI":"10.1088\/1367-2630\/aae8ae","volume":"20","author":"Kalinin","year":"2018","journal-title":"New J. Phys."},{"key":"oe-32-19-33737-R56","doi-asserted-by":"publisher","first-page":"040607","DOI":"10.1103\/PhysRevLett.122.040607","volume":"122","author":"Leleu","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"oe-32-19-33737-R57","doi-asserted-by":"publisher","first-page":"143901","DOI":"10.1103\/PhysRevLett.126.143901","volume":"126","author":"Strinati","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"oe-32-19-33737-R58","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1038\/s42005-021-00655-8","volume":"4","author":"B\u00f6hm","year":"2021","journal-title":"Commun. Phys."},{"key":"oe-32-19-33737-R59","doi-asserted-by":"publisher","first-page":"024057","DOI":"10.1103\/PhysRevApplied.21.024057","volume":"21","author":"Verstraelen","year":"2024","journal-title":"Phys. Rev. Appl."},{"key":"oe-32-19-33737-R60","volume":"2","author":"Hastie","year":"2009"},{"key":"oe-32-19-33737-R61","doi-asserted-by":"publisher","first-page":"2000045","DOI":"10.1002\/qute.202000045","volume":"3","author":"Kako","year":"2020","journal-title":"Adv. Quantum Technol."},{"key":"oe-32-19-33737-R62","doi-asserted-by":"publisher","first-page":"2100077","DOI":"10.1002\/qute.202100077","volume":"4","author":"Reifenstein","year":"2021","journal-title":"Adv. Quantum Technol."},{"key":"oe-32-19-33737-R63","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1038\/s42005-021-00768-0","volume":"4","author":"Leleu","year":"2021","journal-title":"Commun. Phys."},{"key":"oe-32-19-33737-R64","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1038\/s42005-022-00927-x","volume":"5","author":"Inui","year":"2022","journal-title":"Commun. Phys."},{"key":"oe-32-19-33737-R65","doi-asserted-by":"publisher","first-page":"234901","DOI":"10.1063\/5.0176248","volume":"134","author":"Mastiyage Don","year":"2023","journal-title":"J. Appl. Phys."},{"key":"oe-32-19-33737-R67","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1038\/s41534-017-0048-9","volume":"3","author":"Yamamoto","year":"2017","journal-title":"npj Quantum Inf."},{"key":"oe-32-19-33737-R68","doi-asserted-by":"publisher","first-page":"013009","DOI":"10.1103\/PhysRevResearch.4.013009","volume":"4","author":"Ng","year":"2022","journal-title":"Phys. Rev. Res."},{"key":"oe-32-19-33737-R69","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1038\/s41586-018-0551-y","volume":"562","author":"Wang","year":"2018","journal-title":"Nature"},{"key":"oe-32-19-33737-R70","first-page":"2825","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Machine Learning Research"},{"key":"oe-32-19-33737-R72","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1364\/OPTICA.510591","volume":"11","author":"Hamrouni","year":"2024","journal-title":"Optica"},{"key":"oe-32-19-33737-R73","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1364\/OPTICA.449691","volume":"9","author":"Xu","year":"2022","journal-title":"Optica"}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-32-19-33737&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T12:52:31Z","timestamp":1725540751000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-32-19-33737"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,4]]},"references-count":68,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2024]]},"published-print":{"date-parts":[[2024]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.526050","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,4]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.526050","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"23 April 2024","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"19 August 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"4 September 2024","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement","name":"copyright","label":"Copyright"}]}}