{"id":"https://openalex.org/W7164000710","doi":"https://doi.org/10.1103/x7s3-ykb8","title":"Variational matrix product states for combinatorial optimization","display_name":"Variational matrix product states for combinatorial optimization","publication_year":2026,"publication_date":"2026-06-09","ids":{"openalex":"https://openalex.org/W7164000710","doi":"https://doi.org/10.1103/x7s3-ykb8"},"language":"en","primary_location":{"id":"doi:10.1103/x7s3-ykb8","doi":"https://doi.org/10.1103/x7s3-ykb8","is_oa":true,"landing_page_url":"https://doi.org/10.1103/x7s3-ykb8","pdf_url":null,"source":{"id":"https://openalex.org/S4210240247","display_name":"Physical Review Research","issn_l":"2643-1564","issn":["2643-1564"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Research","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1103/x7s3-ykb8","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039068111","display_name":"Guillermo Preisser","orcid":"https://orcid.org/0000-0002-2335-574X","observed_orcids":["https://orcid.org/0000-0002-2335-574X"]},"institutions":[{"id":"https://openalex.org/I4396570559","display_name":"Quantinuum (United Kingdom)","ror":"https://ror.org/0507j3z22","country_code":"GB","type":"company","lineage":["https://openalex.org/I4396570559"]},{"id":"https://openalex.org/I4396570658","display_name":"Quantinuum (United States)","ror":"https://ror.org/03ssvsv78","country_code":"US","type":"company","lineage":["https://openalex.org/I4396570658"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Guillermo Preisser","raw_affiliation_strings":["Quantinuum"],"raw_orcid":"https://orcid.org/0000-0002-2335-574X","affiliations":[{"raw_affiliation_string":"Quantinuum","institution_ids":["https://openalex.org/I4396570559","https://openalex.org/I4396570658"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021382145","display_name":"Conor Mc Keever","orcid":"https://orcid.org/0000-0002-9054-4225","observed_orcids":["https://orcid.org/0000-0002-9054-4225"]},"institutions":[{"id":"https://openalex.org/I4396570559","display_name":"Quantinuum (United Kingdom)","ror":"https://ror.org/0507j3z22","country_code":"GB","type":"company","lineage":["https://openalex.org/I4396570559"]},{"id":"https://openalex.org/I4396570658","display_name":"Quantinuum (United States)","ror":"https://ror.org/03ssvsv78","country_code":"US","type":"company","lineage":["https://openalex.org/I4396570658"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Conor Mc Keever","raw_affiliation_strings":["Quantinuum"],"raw_orcid":"https://orcid.org/0000-0002-9054-4225","affiliations":[{"raw_affiliation_string":"Quantinuum","institution_ids":["https://openalex.org/I4396570559","https://openalex.org/I4396570658"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086082160","display_name":"Michael Lubasch","orcid":"https://orcid.org/0000-0002-2636-9936","observed_orcids":["https://orcid.org/0000-0002-2636-9936"]},"institutions":[{"id":"https://openalex.org/I4396570559","display_name":"Quantinuum (United Kingdom)","ror":"https://ror.org/0507j3z22","country_code":"GB","type":"company","lineage":["https://openalex.org/I4396570559"]},{"id":"https://openalex.org/I4396570658","display_name":"Quantinuum (United States)","ror":"https://ror.org/03ssvsv78","country_code":"US","type":"company","lineage":["https://openalex.org/I4396570658"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Michael Lubasch","raw_affiliation_strings":["Quantinuum"],"raw_orcid":"https://orcid.org/0000-0002-2636-9936","affiliations":[{"raw_affiliation_string":"Quantinuum","institution_ids":["https://openalex.org/I4396570559","https://openalex.org/I4396570658"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2625,"currency":"USD","value_usd":2625},"apc_paid":{"value":2625,"currency":"USD","value_usd":2625},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38204339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"3","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":0.9951000213623047,"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":0.9951000213623047,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.0027000000700354576,"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/T11804","display_name":"Quantum many-body systems","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-product-states","display_name":"matrix product states","score":0.8709999918937683},{"id":"https://openalex.org/keywords/variational-quantum-algorithms","display_name":"variational quantum algorithms","score":0.8069999814033508},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"combinatorial optimization","score":0.9589999914169312},{"id":"https://openalex.org/keywords/quantum-annealing","display_name":"quantum annealing","score":0.7839999794960022},{"id":"https://openalex.org/keywords/iterated-local-search","display_name":"iterated local search","score":0.9240000247955322},{"id":"https://openalex.org/keywords/metaheuristic-optimization","display_name":"metaheuristic optimization","score":0.8820000290870667},{"id":"https://openalex.org/keywords/maximum-cut-problem","display_name":"max-cut problem","score":0.859000027179718},{"id":"https://openalex.org/keywords/quantum-inspired-algorithms","display_name":"quantum-inspired algorithms","score":0.8230000138282776},{"id":"https://openalex.org/keywords/variational-energy-minimization","display_name":"variational energy minimization","score":0.9010000228881836}],"concepts":[{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.49889999628067017},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.439300000667572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4223000109195709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4214000105857849},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.41999998688697815},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.39629998803138733},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3368000090122223},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3246000111103058},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.250900000333786},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2502000033855438}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1103/x7s3-ykb8","doi":"https://doi.org/10.1103/x7s3-ykb8","is_oa":true,"landing_page_url":"https://doi.org/10.1103/x7s3-ykb8","pdf_url":null,"source":{"id":"https://openalex.org/S4210240247","display_name":"Physical Review Research","issn_l":"2643-1564","issn":["2643-1564"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Research","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2512.20613","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2512.20613","pdf_url":"https://arxiv.org/pdf/2512.20613","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:doaj.org/article:532101e25d4b4423bd32d9041d1ca1b9","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/532101e25d4b4423bd32d9041d1ca1b9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Physical Review Research, Vol 8, Iss 3, p 033027 (2026)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2512.20613","doi":"https://doi.org/10.48550/arxiv.2512.20613","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.20613","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1103/x7s3-ykb8","doi":"https://doi.org/10.1103/x7s3-ykb8","is_oa":true,"landing_page_url":"https://doi.org/10.1103/x7s3-ykb8","pdf_url":null,"source":{"id":"https://openalex.org/S4210240247","display_name":"Physical Review Research","issn_l":"2643-1564","issn":["2643-1564"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Research","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W174492123","https://openalex.org/W1840046823","https://openalex.org/W1854468614","https://openalex.org/W1972357767","https://openalex.org/W1983624953","https://openalex.org/W1985123706","https://openalex.org/W2022723663","https://openalex.org/W2033368244","https://openalex.org/W2039122980","https://openalex.org/W2093286150","https://openalex.org/W2096391265","https://openalex.org/W2122816100","https://openalex.org/W2139562712","https://openalex.org/W2159739530","https://openalex.org/W2169440812","https://openalex.org/W2564229214","https://openalex.org/W2798663460","https://openalex.org/W2805842314","https://openalex.org/W2903058119","https://openalex.org/W2949757588","https://openalex.org/W3006255022","https://openalex.org/W3014405689","https://openalex.org/W3040284875","https://openalex.org/W3045710579","https://openalex.org/W3049188247","https://openalex.org/W3111162498","https://openalex.org/W3158966667","https://openalex.org/W3168032916","https://openalex.org/W3194455636","https://openalex.org/W3212169067","https://openalex.org/W4213212652","https://openalex.org/W4282970970","https://openalex.org/W4284883328","https://openalex.org/W4292723404","https://openalex.org/W4295022910","https://openalex.org/W4308632734","https://openalex.org/W4309526890","https://openalex.org/W4313304032","https://openalex.org/W4323047314","https://openalex.org/W4362737055","https://openalex.org/W4377013714","https://openalex.org/W4380434217","https://openalex.org/W4381996727","https://openalex.org/W4393305093","https://openalex.org/W4401567372","https://openalex.org/W4405093149","https://openalex.org/W4405722399","https://openalex.org/W4405904189","https://openalex.org/W4406099298","https://openalex.org/W4410497899","https://openalex.org/W4411375548","https://openalex.org/W4412523690","https://openalex.org/W4415987630","https://openalex.org/W4416407975"],"related_works":["https://openalex.org/W4403445281","https://openalex.org/W7221694894","https://openalex.org/W3038877908","https://openalex.org/W1922954595","https://openalex.org/W2022122405","https://openalex.org/W4408573479","https://openalex.org/W4396819863","https://openalex.org/W2796031795","https://openalex.org/W7158666340","https://openalex.org/W3140392037"],"abstract_inverted_index":{"To":[0],"compute":[1],"approximate":[2,80],"solutions":[3],"for":[4],"combinatorial":[5],"optimization":[6,81],"problems,":[7],"we":[8],"describe":[9],"variational":[10,26,85],"methods":[11],"based":[12],"on":[13,57],"the":[14,41,44,78],"product":[15,20],"state":[16,21],"(PS)":[17],"and":[18,36,83],"matrix":[19],"(MPS)":[22],"ans\u00e4tze.":[23],"We":[24,67],"perform":[25],"energy":[27],"minimization":[28],"with":[29],"respect":[30],"to":[31,63],"a":[32],"quantum":[33,79],"annealing":[34],"Hamiltonian":[35],"utilize":[37],"randomness":[38],"by":[39],"embedding":[40],"approaches":[42],"in":[43],"metaheuristic":[45],"iterated":[46],"local":[47],"search":[48],"(ILS).":[49],"The":[50],"resulting":[51],"quantum-inspired":[52,86],"ILS":[53],"algorithms":[54],"are":[55],"benchmarked":[56],"maximum":[58],"cut":[59],"problems":[60],"of":[61],"up":[62],"50":[64],"000":[65],"variables.":[66],"show":[68],"that":[69],"they":[70],"can":[71],"outperform":[72],"traditional":[73],"(M)PS":[74],"methods,":[75],"classical":[76],"ILS,":[77],"algorithm,":[82],"other":[84],"solvers.":[87]},"counts_by_year":[],"updated_date":"2026-10-27T15:51:10.671819","created_date":"2026-06-10T00:00:00"}