{"id":"https://openalex.org/W2955405219","doi":"https://doi.org/10.1007/s42484-020-00014-w","title":"Accuracy and minor embedding in subqubo decomposition with fully connected large problems: a case study about the number partitioning problem","display_name":"Accuracy and minor embedding in subqubo decomposition with fully connected large problems: a case study about the number partitioning problem","publication_year":2020,"publication_date":"2020-03-19","ids":{"openalex":"https://openalex.org/W2955405219","doi":"https://doi.org/10.1007/s42484-020-00014-w","mag":"2955405219"},"language":"en","primary_location":{"id":"doi:10.1007/s42484-020-00014-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s42484-020-00014-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s42484-020-00014-w.pdf","source":{"id":"https://openalex.org/S4210217596","display_name":"Quantum Machine Intelligence","issn_l":"2524-4906","issn":["2524-4906","2524-4914"],"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":"Quantum Machine Intelligence","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s42484-020-00014-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091423505","display_name":"Luca Asproni","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128559","display_name":"Reply (Italy)","ror":"https://ror.org/03ma9mt41","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210128559"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luca Asproni","raw_affiliation_strings":["Data Reply s.r.l., Via Nizza, 262, 10126, Turin, Italy","Data Reply s.r.l., Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Reply s.r.l., Via Nizza, 262, 10126, Turin, Italy","institution_ids":["https://openalex.org/I4210128559"]},{"raw_affiliation_string":"Data Reply s.r.l., Turin, Italy","institution_ids":["https://openalex.org/I4210128559"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065924670","display_name":"Davide Caputo","orcid":"https://orcid.org/0000-0002-5408-4735"},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]},{"id":"https://openalex.org/I4210128559","display_name":"Reply (Italy)","ror":"https://ror.org/03ma9mt41","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210128559"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Davide Caputo","raw_affiliation_strings":["Data Reply s.r.l., Via Nizza, 262, 10126, Turin, Italy","Department of Mathematics and Physics, University of Salento, Via Arnesano, 73100, Lecce, Italy","Department of Mathematics and Physics, University of Salento, Lecce, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Reply s.r.l., Via Nizza, 262, 10126, Turin, Italy","institution_ids":["https://openalex.org/I4210128559"]},{"raw_affiliation_string":"Department of Mathematics and Physics, University of Salento, Via Arnesano, 73100, Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Department of Mathematics and Physics, University of Salento, Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113503067","display_name":"Blanca Silva","orcid":"https://orcid.org/0009-0003-3110-1322"},"institutions":[{"id":"https://openalex.org/I4210128559","display_name":"Reply (Italy)","ror":"https://ror.org/03ma9mt41","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210128559"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Blanca Silva","raw_affiliation_strings":["Data Reply s.r.l., Via Nizza, 262, 10126, Turin, Italy","Data Reply s.r.l., Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Reply s.r.l., Via Nizza, 262, 10126, Turin, Italy","institution_ids":["https://openalex.org/I4210128559"]},{"raw_affiliation_string":"Data Reply s.r.l., Turin, Italy","institution_ids":["https://openalex.org/I4210128559"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049575993","display_name":"Giovanni Fazzi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128559","display_name":"Reply (Italy)","ror":"https://ror.org/03ma9mt41","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210128559"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giovanni Fazzi","raw_affiliation_strings":["Quantum Computing Community Of Practice, Reply S.p.A., Corso Francia, 110, 10143, Turin, Italy","Quantum Computing Community Of Practice, Reply S.p.A., Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quantum Computing Community Of Practice, Reply S.p.A., Corso Francia, 110, 10143, Turin, Italy","institution_ids":["https://openalex.org/I4210128559"]},{"raw_affiliation_string":"Quantum Computing Community Of Practice, Reply S.p.A., Turin, Italy","institution_ids":["https://openalex.org/I4210128559"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043280581","display_name":"Marco Magagnini","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128559","display_name":"Reply (Italy)","ror":"https://ror.org/03ma9mt41","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210128559"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Magagnini","raw_affiliation_strings":["Quantum Computing Community Of Practice, Reply S.p.A., Corso Francia, 110, 10143, Turin, Italy","Quantum Computing Community Of Practice, Reply S.p.A., Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quantum Computing Community Of Practice, Reply S.p.A., Corso Francia, 110, 10143, Turin, Italy","institution_ids":["https://openalex.org/I4210128559"]},{"raw_affiliation_string":"Quantum Computing Community Of Practice, Reply S.p.A., Turin, Italy","institution_ids":["https://openalex.org/I4210128559"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5091423505"],"corresponding_institution_ids":["https://openalex.org/I4210128559"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00180901,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13104","display_name":"Chemical and Physical Properties of Materials","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13104","display_name":"Chemical and Physical Properties of Materials","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9675999879837036,"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/T12044","display_name":"Advanced Physical and Chemical Molecular Interactions","score":0.9645000100135803,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-annealing","display_name":"Quantum annealing","score":0.9078879356384277},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7168903350830078},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.7140905857086182},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6741491556167603},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.6526008248329163},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6018115878105164},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.5593191981315613},{"id":"https://openalex.org/keywords/workflow","display_name":"Workflow","score":0.5572505593299866},{"id":"https://openalex.org/keywords/suite","display_name":"Suite","score":0.5484097003936768},{"id":"https://openalex.org/keywords/simulated-annealing","display_name":"Simulated annealing","score":0.5253281593322754},{"id":"https://openalex.org/keywords/quadratic-unconstrained-binary-optimization","display_name":"Quadratic unconstrained binary optimization","score":0.4145032465457916},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3920360803604126},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36437857151031494},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3503198027610779},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.34421995282173157},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.336467981338501},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23765835165977478},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13489693403244019},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11155179142951965},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09152358770370483}],"concepts":[{"id":"https://openalex.org/C90408235","wikidata":"https://www.wikidata.org/wiki/Q938141","display_name":"Quantum annealing","level":4,"score":0.9078879356384277},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7168903350830078},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.7140905857086182},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6741491556167603},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6526008248329163},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6018115878105164},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.5593191981315613},{"id":"https://openalex.org/C177212765","wikidata":"https://www.wikidata.org/wiki/Q627335","display_name":"Workflow","level":2,"score":0.5572505593299866},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.5484097003936768},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.5253281593322754},{"id":"https://openalex.org/C177179195","wikidata":"https://www.wikidata.org/wiki/Q7268372","display_name":"Quadratic unconstrained binary optimization","level":4,"score":0.4145032465457916},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3920360803604126},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36437857151031494},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3503198027610779},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.34421995282173157},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.336467981338501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23765835165977478},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13489693403244019},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11155179142951965},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09152358770370483},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s42484-020-00014-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s42484-020-00014-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s42484-020-00014-w.pdf","source":{"id":"https://openalex.org/S4210217596","display_name":"Quantum Machine Intelligence","issn_l":"2524-4906","issn":["2524-4906","2524-4914"],"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":"Quantum Machine Intelligence","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1907.01892","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.01892","pdf_url":"https://arxiv.org/pdf/1907.01892","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"doi:10.48550/arxiv.1907.01892","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1907.01892","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2955405219","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.1007/s42484-020-00014-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s42484-020-00014-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s42484-020-00014-w.pdf","source":{"id":"https://openalex.org/S4210217596","display_name":"Quantum Machine Intelligence","issn_l":"2524-4906","issn":["2524-4906","2524-4914"],"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":"Quantum Machine Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320318328","display_name":"Universities Space Research Association","ror":"https://ror.org/043pgqy52"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2955405219.pdf","grobid_xml":"https://content.openalex.org/works/W2955405219.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W61065943","https://openalex.org/W641266820","https://openalex.org/W1488590474","https://openalex.org/W1564295073","https://openalex.org/W1964730958","https://openalex.org/W2037618925","https://openalex.org/W2039122980","https://openalex.org/W2066297895","https://openalex.org/W2340276704","https://openalex.org/W2605422054","https://openalex.org/W2616867685","https://openalex.org/W2616974032","https://openalex.org/W2750232680","https://openalex.org/W2769474857","https://openalex.org/W2770478968","https://openalex.org/W2771114131","https://openalex.org/W2785399333","https://openalex.org/W2887462821","https://openalex.org/W2897914876","https://openalex.org/W2962964603","https://openalex.org/W2963757591","https://openalex.org/W6638347121"],"related_works":["https://openalex.org/W2755987512","https://openalex.org/W3110080432","https://openalex.org/W2912323481","https://openalex.org/W3101797062","https://openalex.org/W2498041627","https://openalex.org/W2462100444","https://openalex.org/W3024374568","https://openalex.org/W3080744988","https://openalex.org/W2949180570","https://openalex.org/W2398368864","https://openalex.org/W3122401610","https://openalex.org/W3199647924","https://openalex.org/W2744918591","https://openalex.org/W2516615552","https://openalex.org/W2986094212","https://openalex.org/W3124048260","https://openalex.org/W2520150327","https://openalex.org/W3199854653","https://openalex.org/W47122707","https://openalex.org/W3048188227"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"work,":[3],"we":[4,29,79,103,111],"investigate":[5,104],"the":[6,15,19,31,34,39,63,75,81,85,96,99,106,116,121,126,130,138],"capabilities":[7],"of":[8,33,53,62,69,84,95],"a":[9,43,135],"hybrid":[10],"quantum-classical":[11,86],"procedure":[12],"to":[13,37,114],"explore":[14],"solution":[16],"space":[17],"using":[18],"D-Wave":[20,107],"2000":[21],"Q":[22],"T":[23],"M":[24],"quantum":[25,35],"annealer":[26],"device.":[27],"Here,":[28],"study":[30],"ability":[32],"hardware":[36],"solve":[38],"number":[40],"partitioning":[41],"problem,":[42],"well-known":[44],"NP-hard":[45],"optimization":[46],"model":[47],"that":[48,128],"poses":[49],"some":[50],"challenges":[51],"typical":[52],"those":[54],"encountered":[55],"in":[56,67,92,120,137],"real-world":[57],"applications.":[58],"This":[59],"represents":[60],"one":[61],"most":[64,93,100],"complex":[65,101],"scenario":[66],"terms":[68],"qubits":[70],"connectivity":[71],"and,":[72],"by":[73,124],"increasing":[74],"input":[76],"problem":[77],"size,":[78],"analyze":[80],"scaling":[82],"properties":[83],"workflow.":[87],"We":[88],"find":[89,115],"remarkable":[90],"results":[91],"instances":[94],"model;":[97],"for":[98],"ones,":[102],"further":[105],"Hybrid":[108],"suite.":[109],"Specifically,":[110],"were":[112],"able":[113],"optimal":[117],"solutions":[118],"even":[119],"worst":[122],"cases":[123],"fine-tuning":[125],"parameters":[127],"schedule":[129],"annealing":[131,139],"time":[132],"and":[133],"allowing":[134],"pause":[136],"cycle.":[140]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}