{"id":"https://openalex.org/W2710900611","doi":"https://doi.org/10.1073/pnas.1711456115","title":"Efficiency of quantum vs. classical annealing in nonconvex learning problems","display_name":"Efficiency of quantum vs. classical annealing in nonconvex learning problems","publication_year":2018,"publication_date":"2018-01-30","ids":{"openalex":"https://openalex.org/W2710900611","doi":"https://doi.org/10.1073/pnas.1711456115","mag":"2710900611","pmid":"https://pubmed.ncbi.nlm.nih.gov/29382764"},"language":"en","primary_location":{"id":"doi:10.1073/pnas.1711456115","is_oa":false,"landing_page_url":"https://doi.org/10.1073/pnas.1711456115","pdf_url":null,"source":{"id":"https://openalex.org/S125754415","display_name":"Proceedings of the National Academy of Sciences","issn_l":"0027-8424","issn":["0027-8424","1091-6490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320052","host_organization_name":"National Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310320052"],"host_organization_lineage_names":["National Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1706.08470","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028083013","display_name":"Carlo Baldassi","orcid":"https://orcid.org/0000-0002-5451-8388"},"institutions":[{"id":"https://openalex.org/I4210099850","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Torino","ror":"https://ror.org/01vj6ck58","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210099850"]},{"id":"https://openalex.org/I71209653","display_name":"Bocconi University","ror":"https://ror.org/05crjpb27","country_code":"IT","type":"education","lineage":["https://openalex.org/I71209653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carlo Baldassi","raw_affiliation_strings":["Bocconi Institute for Data Science and Analytics, Bocconi University, 20136 Milan, Italy;","Istituto Nazionale di Fisica Nucleare, Sezione di Torino, 10125 Turin, Italy;"],"raw_orcid":"https://orcid.org/0000-0002-5451-8388","affiliations":[{"raw_affiliation_string":"Bocconi Institute for Data Science and Analytics, Bocconi University, 20136 Milan, Italy;","institution_ids":["https://openalex.org/I71209653"]},{"raw_affiliation_string":"Istituto Nazionale di Fisica Nucleare, Sezione di Torino, 10125 Turin, Italy;","institution_ids":["https://openalex.org/I4210099850"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041685522","display_name":"Riccardo Zecchina","orcid":"https://orcid.org/0000-0002-1221-5207"},"institutions":[{"id":"https://openalex.org/I12323705","display_name":"The Abdus Salam International Centre for Theoretical Physics (ICTP)","ror":"https://ror.org/009gyvm78","country_code":"IT","type":"facility","lineage":["https://openalex.org/I12323705","https://openalex.org/I1286959531","https://openalex.org/I1293226324","https://openalex.org/I2801247003"]},{"id":"https://openalex.org/I71209653","display_name":"Bocconi University","ror":"https://ror.org/05crjpb27","country_code":"IT","type":"education","lineage":["https://openalex.org/I71209653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Riccardo Zecchina","raw_affiliation_strings":["Bocconi Institute for Data Science and Analytics, Bocconi University, 20136 Milan, Italy;","Condensed Matter and Statistical Physics Group, International Centre for Theoretical Physics, 34151 Trieste, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bocconi Institute for Data Science and Analytics, Bocconi University, 20136 Milan, Italy;","institution_ids":["https://openalex.org/I71209653"]},{"raw_affiliation_string":"Condensed Matter and Statistical Physics Group, International Centre for Theoretical Physics, 34151 Trieste, Italy","institution_ids":["https://openalex.org/I12323705"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.372,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.95152936,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"115","issue":"7","first_page":"1457","last_page":"1462"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9932000041007996,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9896000027656555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-annealing","display_name":"Quantum annealing","score":0.6899369359016418},{"id":"https://openalex.org/keywords/annealing","display_name":"Annealing (glass)","score":0.5545036792755127},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.543336808681488},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39132779836654663},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37269920110702515},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3650014400482178},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.33680659532546997},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.27100199460983276},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24614489078521729},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.1297627091407776},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.11442205309867859}],"concepts":[{"id":"https://openalex.org/C90408235","wikidata":"https://www.wikidata.org/wiki/Q938141","display_name":"Quantum annealing","level":4,"score":0.6899369359016418},{"id":"https://openalex.org/C2777855556","wikidata":"https://www.wikidata.org/wiki/Q4339544","display_name":"Annealing (glass)","level":2,"score":0.5545036792755127},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.543336808681488},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39132779836654663},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37269920110702515},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3650014400482178},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.33680659532546997},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.27100199460983276},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24614489078521729},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.1297627091407776},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.11442205309867859}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1073/pnas.1711456115","is_oa":false,"landing_page_url":"https://doi.org/10.1073/pnas.1711456115","pdf_url":null,"source":{"id":"https://openalex.org/S125754415","display_name":"Proceedings of the National Academy of Sciences","issn_l":"0027-8424","issn":["0027-8424","1091-6490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320052","host_organization_name":"National Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310320052"],"host_organization_lineage_names":["National Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences","raw_type":"journal-article"},{"id":"pmid:29382764","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29382764","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences of the United States of America","raw_type":null},{"id":"pmh:oai:arXiv.org:1706.08470","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.08470","pdf_url":"https://arxiv.org/pdf/1706.08470","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,"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:pubmedcentral.nih.gov:5816144","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5816144","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc Natl Acad Sci U S A","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1706.08470","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.08470","pdf_url":"https://arxiv.org/pdf/1706.08470","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,"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"},"sustainable_development_goals":[{"score":0.9100000262260437,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G6607879451","display_name":null,"funder_award_id":"N00014-17-1-2569","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7272902013","display_name":null,"funder_award_id":"N00014-17-1-2569","funder_id":"https://openalex.org/F4320332923","funder_display_name":"U.S. Navy"}],"funders":[{"id":"https://openalex.org/F4320332923","display_name":"U.S. Navy","ror":"https://ror.org/03ar0mv07"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W174492123","https://openalex.org/W567708786","https://openalex.org/W1607198972","https://openalex.org/W1967364564","https://openalex.org/W1981659415","https://openalex.org/W1983624953","https://openalex.org/W1984793731","https://openalex.org/W1987116538","https://openalex.org/W1989283826","https://openalex.org/W2001541371","https://openalex.org/W2007473024","https://openalex.org/W2013520638","https://openalex.org/W2024860775","https://openalex.org/W2025397511","https://openalex.org/W2027368911","https://openalex.org/W2028918948","https://openalex.org/W2029163489","https://openalex.org/W2031828766","https://openalex.org/W2033606703","https://openalex.org/W2034230381","https://openalex.org/W2036759514","https://openalex.org/W2042127289","https://openalex.org/W2058599268","https://openalex.org/W2060478085","https://openalex.org/W2060719094","https://openalex.org/W2076227063","https://openalex.org/W2083773133","https://openalex.org/W2085138324","https://openalex.org/W2088175653","https://openalex.org/W2090946156","https://openalex.org/W2094756709","https://openalex.org/W2105614108","https://openalex.org/W2117762142","https://openalex.org/W2172308869","https://openalex.org/W2211979669","https://openalex.org/W2262347687","https://openalex.org/W2262732936","https://openalex.org/W2436219157","https://openalex.org/W2469525139","https://openalex.org/W2517648041","https://openalex.org/W2523060838","https://openalex.org/W2524428287","https://openalex.org/W2559655401","https://openalex.org/W2560369697","https://openalex.org/W2566505556","https://openalex.org/W2919115771","https://openalex.org/W2950894517","https://openalex.org/W3098571064","https://openalex.org/W3098762758","https://openalex.org/W3099399833","https://openalex.org/W3100133284","https://openalex.org/W3100721033","https://openalex.org/W3103299518","https://openalex.org/W3103710211","https://openalex.org/W3104611581","https://openalex.org/W3106141570","https://openalex.org/W3111616562","https://openalex.org/W3140968660","https://openalex.org/W4294351759","https://openalex.org/W4296269336","https://openalex.org/W4298327625","https://openalex.org/W6658326963","https://openalex.org/W6787348142"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2710900611","https://openalex.org/W2606103374","https://openalex.org/W4379933616","https://openalex.org/W3165476442","https://openalex.org/W4304092472","https://openalex.org/W2810672418","https://openalex.org/W4386982579","https://openalex.org/W4310832015","https://openalex.org/W2963447708"],"abstract_inverted_index":{"Quantum":[0],"annealers":[1,104],"aim":[2],"at":[3],"solving":[4],"nonconvex":[5,59],"optimization":[6,38,60],"problems":[7,61,82],"by":[8,94],"exploiting":[9],"cooperative":[10],"tunneling":[11,49],"effects":[12],"to":[13,47,55,86,111],"escape":[14],"local":[15,95],"minima.":[16],"The":[17],"underlying":[18],"idea":[19],"consists":[20],"of":[21,35,58,81,101,115],"designing":[22],"a":[23,42,78],"classical":[24,102],"energy":[25,90],"function":[26],"whose":[27],"ground":[28],"states":[29],"are":[30,84,92],"the":[31,36],"sought":[32],"optimal":[33,116],"solutions":[34],"original":[37],"problem":[39],"and":[40],"add":[41],"controllable":[43],"quantum":[44,64,107],"transverse":[45],"field":[46],"generate":[48],"processes.":[50],"A":[51],"key":[52],"challenge":[53],"is":[54],"identify":[56],"classes":[57],"for":[62,77],"which":[63,83],"annealing":[65,70,108],"remains":[66],"efficient":[67],"while":[68,105],"thermal":[69,103],"fails.":[71],"We":[72],"show":[73],"that":[74,97],"this":[75],"happens":[76],"wide":[79],"class":[80],"central":[85],"machine":[87],"learning.":[88],"Their":[89],"landscapes":[91],"dominated":[93],"minima":[96],"cause":[98],"exponential":[99],"slowdown":[100],"simulated":[106],"converges":[109],"efficiently":[110],"rare":[112],"dense":[113],"regions":[114],"solutions.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":6}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
