{"id":"https://openalex.org/W2980961571","doi":"https://doi.org/10.22331/q-2022-07-07-759","title":"The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size","display_name":"The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size","publication_year":2022,"publication_date":"2022-07-07","ids":{"openalex":"https://openalex.org/W2980961571","doi":"https://doi.org/10.22331/q-2022-07-07-759","mag":"2980961571"},"language":"en","primary_location":{"id":"doi:10.22331/q-2022-07-07-759","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-07-07-759","pdf_url":"https://quantum-journal.org/papers/q-2022-07-07-759/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"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","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2022-07-07-759/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036253306","display_name":"Edward Farhi","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edward Farhi","raw_affiliation_strings":["Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA","Google Inc., Venice, CA 90291, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Google Inc., Venice, CA 90291, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103341826","display_name":"Jeffrey Goldstone","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeffrey Goldstone","raw_affiliation_strings":["Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022783879","display_name":"Sam Gutmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sam Gutmann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061621981","display_name":"Leo Zhou","orcid":"https://orcid.org/0000-0001-7598-8621"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leo Zhou","raw_affiliation_strings":["Department of Physics, Harvard University, Cambridge, MA 02138, USA","Google Inc., Venice, CA 90291, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Harvard University, Cambridge, MA 02138, USA","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"Google Inc., Venice, CA 90291, USA","institution_ids":["https://openalex.org/I1291425158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":23.0125,"has_fulltext":true,"cited_by_count":241,"citation_normalized_percentile":{"value":0.99629516,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"6","issue":null,"first_page":"759","last_page":"759"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9970999956130981,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9905999898910522,"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/algorithm","display_name":"Algorithm","score":0.6826274394989014},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5565313696861267},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4850260615348816},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4436522126197815},{"id":"https://openalex.org/keywords/energy-minimization","display_name":"Energy minimization","score":0.4423770010471344},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35006242990493774},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34623169898986816},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3227294087409973},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26923125982284546},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.24195051193237305},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2369970679283142},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.20496094226837158}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6826274394989014},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5565313696861267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4850260615348816},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4436522126197815},{"id":"https://openalex.org/C14961307","wikidata":"https://www.wikidata.org/wiki/Q5377176","display_name":"Energy minimization","level":2,"score":0.4423770010471344},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35006242990493774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34623169898986816},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3227294087409973},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26923125982284546},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.24195051193237305},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2369970679283142},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.20496094226837158}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2022-07-07-759","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-07-07-759","pdf_url":"https://quantum-journal.org/papers/q-2022-07-07-759/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"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","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1910.08187","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.08187","pdf_url":"https://arxiv.org/pdf/1910.08187","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:doaj.org/article:00569b43a08a4dd2a7eadbecd4ea4283","is_oa":true,"landing_page_url":"https://doaj.org/article/00569b43a08a4dd2a7eadbecd4ea4283","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 6, p 759 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2022-07-07-759","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-07-07-759","pdf_url":"https://quantum-journal.org/papers/q-2022-07-07-759/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"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","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.800000011920929,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G2077426331","display_name":null,"funder_award_id":"W911NF-17-1-0433","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2980961571.pdf","grobid_xml":"https://content.openalex.org/works/W2980961571.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1568345435","https://openalex.org/W1752349928","https://openalex.org/W2077168589","https://openalex.org/W2095058792","https://openalex.org/W2216459995","https://openalex.org/W2225611404","https://openalex.org/W2738325034","https://openalex.org/W2794444783","https://openalex.org/W2901444101","https://openalex.org/W2903058119","https://openalex.org/W2904281284","https://openalex.org/W2906886359","https://openalex.org/W2915222866","https://openalex.org/W2971940014","https://openalex.org/W2987043130","https://openalex.org/W3003864485","https://openalex.org/W3089060063","https://openalex.org/W3100894865","https://openalex.org/W3104170093","https://openalex.org/W3104396616","https://openalex.org/W3122217484","https://openalex.org/W3209534835","https://openalex.org/W4210422269","https://openalex.org/W4231567523","https://openalex.org/W4289125053","https://openalex.org/W4289283645"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W4300899577","https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W1973978937","https://openalex.org/W121594594","https://openalex.org/W2784911598","https://openalex.org/W2914578401"],"abstract_inverted_index":{"The":[0],"Quantum":[1],"Approximate":[2],"Optimization":[3],"Algorithm":[4],"(QAOA)":[5],"is":[6,78,124,234,257],"a":[7,79,87,98,125,146,156,173,230,258],"general-purpose":[8],"algorithm":[9,32,82,227],"for":[10,97,148,239,261,273],"combinatorial":[11],"optimization":[12],"problems":[13,280],"whose":[14,218],"performance":[15,118,276],"can":[16,34,63,91,169,248,268],"only":[17],"improve":[18],"with":[19,72,119,175],"the":[20,54,58,102,109,120,133,137,141,149,153,159,164,180,189,194,213,263],"number":[21],"of":[22,69,101,136,152,158,212,270],"layers":[23],"p":[24],".":[25],"While":[26],"QAOA":[27,55,138,161,190,214],"holds":[28],"promise":[29],"as":[30,66,155,208],"an":[31,94,226,243],"that":[33,128,168,188],"be":[35,64,170,269],"run":[36],"on":[37,172,229,242,277],"near-term":[38],"quantum":[39,231],"computers,":[40],"its":[41,117,275],"computational":[42],"power":[43],"has":[44],"not":[45],"been":[46],"fully":[47],"explored.":[48],"In":[49],"this":[50],"work,":[51],"we":[52,200,247,254],"study":[53],"applied":[56,139],"to":[57,105,115,131,140,183,206,237],"Sherrington-Kirkpatrick":[59],"(SK)":[60],"model,":[61],"which":[62],"understood":[65],"energy":[67,135],"minimization":[68],"n":[70],"spins":[71],"all-to-all":[73],"random":[74],"signed":[75],"couplings.":[76],"There":[77],"recent":[80],"classical":[81,282],"by":[83],"Montanari":[84],"that,":[85],"assuming":[86],"widely":[88],"believed":[89],"conjecture,":[90],"efficiently":[92],"find":[93,187],"approximate":[95],"solution":[96],"typical":[99],"instance":[100],"SK":[103,142],"model":[104],"within":[106],"(1\u2212\u03f5)":[107],"times":[108],"ground":[110],"state":[111],"energy.":[112],"We":[113,144,178],"hope":[114],"match":[116],"QAOA.Our":[121],"main":[122],"result":[123],"novel":[126],"technique":[127],"allows":[129],"us":[130],"evaluate":[132,179],"typical-instance":[134],"model.":[143],"produce":[145,216],"formula":[147,181],"expected":[150],"value":[151],"energy,":[154],"function":[157],"2p":[160],"parameters,":[162],"in":[163,251],"infinite":[165],"size":[166],"limit":[167],"evaluated":[171],"computer":[174],"O(16p)":[176],"complexity.":[177],"up":[182],"p=12":[184],",":[185,210],"and":[186,265],"at":[191,221],"p=11":[192],"outperforms":[193],"standard":[195],"semidefinite":[196],"programming":[197],"algorithm.":[198],"Moreover,":[199],"show":[201],"concentration:":[202],"With":[203],"probability":[204],"tending":[205],"one":[207],"n\u2192\u221e":[209],"measurements":[211],"will":[215],"strings":[217],"energies":[219],"concentrate":[220],"our":[222,266],"calculated":[223],"value.":[224],"As":[225],"running":[228],"computer,":[232],"there":[233],"no":[235],"need":[236],"search":[238],"optimal":[240],"parameters":[241],"instance-by-instance":[244],"basis":[245],"since":[246],"determine":[249],"them":[250],"advance.":[252],"What":[253],"have":[255],"here":[256],"new":[259],"framework":[260],"analyzing":[262],"QAOA,":[264],"techniques":[267],"broad":[271],"interest":[272],"evaluating":[274],"more":[278],"general":[279],"where":[281],"algorithms":[283],"may":[284],"fail.":[285]},"counts_by_year":[{"year":2026,"cited_by_count":27},{"year":2025,"cited_by_count":41},{"year":2024,"cited_by_count":63},{"year":2023,"cited_by_count":55},{"year":2022,"cited_by_count":26},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":12}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2019-10-25T00:00:00"}
