{"id":"https://openalex.org/W4409540906","doi":"https://doi.org/10.1007/s10732-025-09556-3","title":"Efficient solution of the number partitioning problem on a quantum annealer: a hybrid quantum-classical decomposition approach","display_name":"Efficient solution of the number partitioning problem on a quantum annealer: a hybrid quantum-classical decomposition approach","publication_year":2025,"publication_date":"2025-04-17","ids":{"openalex":"https://openalex.org/W4409540906","doi":"https://doi.org/10.1007/s10732-025-09556-3"},"language":"en","primary_location":{"id":"doi:10.1007/s10732-025-09556-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10732-025-09556-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10732-025-09556-3.pdf","source":{"id":"https://openalex.org/S111418578","display_name":"Journal of Heuristics","issn_l":"1381-1231","issn":["1381-1231","1572-9397"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Heuristics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10732-025-09556-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063228895","display_name":"Zongji Li","orcid":"https://orcid.org/0000-0003-1683-8388"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Zongji Li","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017345166","display_name":"Tobias Seidel","orcid":"https://orcid.org/0000-0002-0612-6072"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias Seidel","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062999924","display_name":"Dominik Leib","orcid":"https://orcid.org/0009-0005-8950-2000"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dominik Leib","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000192875","display_name":"Michael Bortz","orcid":"https://orcid.org/0000-0001-8169-2907"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Bortz","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019819029","display_name":"Raoul Heese","orcid":"https://orcid.org/0000-0001-7479-3339"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Raoul Heese","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5063228895"],"corresponding_institution_ids":["https://openalex.org/I3019415892"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":7.2362,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.96373991,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"31","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9739000201225281,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.6873837113380432},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5701016187667847},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4786176085472107},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3711148500442505},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3615175187587738},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2706565856933594},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23004698753356934},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.12284120917320251}],"concepts":[{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6873837113380432},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5701016187667847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4786176085472107},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3711148500442505},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3615175187587738},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2706565856933594},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23004698753356934},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.12284120917320251},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10732-025-09556-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10732-025-09556-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10732-025-09556-3.pdf","source":{"id":"https://openalex.org/S111418578","display_name":"Journal of Heuristics","issn_l":"1381-1231","issn":["1381-1231","1572-9397"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Heuristics","raw_type":"journal-article"},{"id":"pmh:oai:econstor.eu:10419/323325","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/323325","pdf_url":"https://www.econstor.eu/bitstream/10419/323325/1/10732_2025_Article_9556.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:RePEc:spr:joheur:v:31:y:2025:i:2:d:10.1007_s10732-025-09556-3","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10732-025-09556-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/488422","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/488422","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.1007/s10732-025-09556-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10732-025-09556-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10732-025-09556-3.pdf","source":{"id":"https://openalex.org/S111418578","display_name":"Journal of Heuristics","issn_l":"1381-1231","issn":["1381-1231","1572-9397"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Heuristics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7225624288","display_name":null,"funder_award_id":"This work was","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"}],"funders":[{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409540906.pdf","grobid_xml":"https://content.openalex.org/works/W4409540906.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1631535324","https://openalex.org/W1984481156","https://openalex.org/W1987615786","https://openalex.org/W2005079828","https://openalex.org/W2016357237","https://openalex.org/W2038536573","https://openalex.org/W2067612530","https://openalex.org/W2076043677","https://openalex.org/W2083941921","https://openalex.org/W2090865599","https://openalex.org/W2099081893","https://openalex.org/W2116667771","https://openalex.org/W2401610261","https://openalex.org/W2564229214","https://openalex.org/W2754868542","https://openalex.org/W2781738013","https://openalex.org/W2888235139","https://openalex.org/W2901983189","https://openalex.org/W2907782024","https://openalex.org/W2914574155","https://openalex.org/W2948980992","https://openalex.org/W2964323614","https://openalex.org/W3011611734","https://openalex.org/W3030209423","https://openalex.org/W3086040199","https://openalex.org/W3098268180","https://openalex.org/W3099107376","https://openalex.org/W3100931082","https://openalex.org/W3101448925","https://openalex.org/W3105085469","https://openalex.org/W3151893275","https://openalex.org/W3184433993","https://openalex.org/W3192498354","https://openalex.org/W4206549951","https://openalex.org/W4226006885","https://openalex.org/W4255654664","https://openalex.org/W4285293325","https://openalex.org/W4310709557","https://openalex.org/W4317756920","https://openalex.org/W4319736340","https://openalex.org/W4384282416","https://openalex.org/W4389469953","https://openalex.org/W4409540906","https://openalex.org/W6968296464"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Abstract":[0],"Current":[1],"quantum":[2,39,109,153],"computers":[3],"can":[4],"only":[5],"solve":[6,80,142],"optimization":[7],"problems":[8],"of":[9,91,129],"a":[10,47,72,76,88,98,108,146],"very":[11],"limited":[12],"size.":[13],"For":[14],"larger":[15,132],"problems,":[16],"decomposition":[17,56,100],"methods":[18,57],"are":[19,34,44,105],"required":[20],"in":[21],"which":[22,104],"the":[23,38,51,61,81,114,130,150],"original":[24,52,131],"problem":[25,63,85,124],"is":[26,95],"broken":[27],"down":[28],"into":[29,46,65,101,116],"several":[30],"smaller":[31,102],"sub-problems.":[32],"These":[33],"then":[35,112],"solved":[36,106],"on":[37,107],"computer":[40],"and":[41,111],"their":[42],"solutions":[43],"recombined":[45],"final":[48],"solution":[49,128],"for":[50],"problem.":[53,133],"Often,":[54],"these":[55],"do":[58],"not":[59],"take":[60],"specific":[62],"structure":[64],"account.":[66],"In":[67],"this":[68,122],"paper,":[69],"we":[70],"present":[71],"tailored":[73],"method":[74,139],"using":[75,149],"divide-and-conquer":[77],"strategy":[78],"to":[79,96,141],"2-way":[82],"Number":[83],"partitioning":[84],"(NPP)":[86],"with":[87,144],"large":[89],"number":[90],"variables.":[92],"The":[93],"idea":[94],"perform":[97],"specialized":[99],"NPPs,":[103],"computer,":[110],"recombine":[113],"results":[115],"another":[117],"small":[118],"auxiliary":[119,123],"NPP.":[120],"Solving":[121],"yields":[125],"an":[126],"approximate":[127],"We":[134],"experimentally":[135],"verify":[136],"that":[137],"our":[138],"allows":[140],"NPPs":[143],"over":[145],"thousand":[147],"variables":[148],"D-Wave":[151],"Advantage":[152],"annealer":[154],"(Advantage_system6.4).":[155]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-04-18T00:00:00"}