{"id":"https://openalex.org/W4394821752","doi":"https://doi.org/10.1137/22m1514581","title":"A Copositive Framework for Analysis of Hybrid Ising-Classical Algorithms","display_name":"A Copositive Framework for Analysis of Hybrid Ising-Classical Algorithms","publication_year":2024,"publication_date":"2024-04-15","ids":{"openalex":"https://openalex.org/W4394821752","doi":"https://doi.org/10.1137/22m1514581"},"language":"en","primary_location":{"id":"doi:10.1137/22m1514581","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1514581","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028821454","display_name":"Robin Brown","orcid":"https://orcid.org/0000-0002-5317-1669"},"institutions":[{"id":"https://openalex.org/I143663144","display_name":"Research Institute for Advanced Computer Science","ror":"https://ror.org/022qmyy53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1329765538","https://openalex.org/I143663144"]},{"id":"https://openalex.org/I2800713631","display_name":"NASA Research Park","ror":"https://ror.org/04hccab49","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280536761","https://openalex.org/I2800713631","https://openalex.org/I4210124779"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robin Brown","raw_affiliation_strings":["Autonomous Systems Laboratory, Stanford University, Stanford, CA 94305 USA; USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA 94043 USA; NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA","Autonomous Systems Laboratory, Stanford University, Stanford, CA 94305 USA","NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA"],"affiliations":[{"raw_affiliation_string":"Autonomous Systems Laboratory, Stanford University, Stanford, CA 94305 USA; USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA 94043 USA; NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA","institution_ids":["https://openalex.org/I143663144","https://openalex.org/I2800713631"]},{"raw_affiliation_string":"Autonomous Systems Laboratory, Stanford University, Stanford, CA 94305 USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA","institution_ids":["https://openalex.org/I2800713631"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010174244","display_name":"David E. Bernal","orcid":"https://orcid.org/0000-0002-8308-5016"},"institutions":[{"id":"https://openalex.org/I143663144","display_name":"Research Institute for Advanced Computer Science","ror":"https://ror.org/022qmyy53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1329765538","https://openalex.org/I143663144"]},{"id":"https://openalex.org/I2800713631","display_name":"NASA Research Park","ror":"https://ror.org/04hccab49","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280536761","https://openalex.org/I2800713631","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David E. Bernal Neira","raw_affiliation_strings":["Corresponding author. USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA 94043 USA; NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA; Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47907 USA","NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA"],"affiliations":[{"raw_affiliation_string":"Corresponding author. USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA 94043 USA; NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA; Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47907 USA","institution_ids":["https://openalex.org/I143663144","https://openalex.org/I2800713631"]},{"raw_affiliation_string":"NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA","institution_ids":["https://openalex.org/I2800713631"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102985745","display_name":"Davide Venturelli","orcid":"https://orcid.org/0000-0003-0452-7603"},"institutions":[{"id":"https://openalex.org/I143663144","display_name":"Research Institute for Advanced Computer Science","ror":"https://ror.org/022qmyy53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1329765538","https://openalex.org/I143663144"]},{"id":"https://openalex.org/I2800713631","display_name":"NASA Research Park","ror":"https://ror.org/04hccab49","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280536761","https://openalex.org/I2800713631","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Davide Venturelli","raw_affiliation_strings":["USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA 94043 USA; NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA","NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA"],"affiliations":[{"raw_affiliation_string":"USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA 94043 USA; NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA","institution_ids":["https://openalex.org/I143663144","https://openalex.org/I2800713631"]},{"raw_affiliation_string":"NASA Quantum Artificial Intelligence Laboratory (QuAIL), Moffett Field, CA 94035 USA","institution_ids":["https://openalex.org/I2800713631"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050003000","display_name":"Marco Pavone","orcid":"https://orcid.org/0000-0002-0206-4337"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marco Pavone","raw_affiliation_strings":["Autonomous Systems Laboratory, Stanford University, Stanford, CA 94305 USA"],"affiliations":[{"raw_affiliation_string":"Autonomous Systems Laboratory, Stanford University, Stanford, CA 94305 USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5028821454"],"corresponding_institution_ids":["https://openalex.org/I143663144","https://openalex.org/I2800713631","https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":0.683,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72914086,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"34","issue":"2","first_page":"1455","last_page":"1489"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"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":1.0,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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":0.9686999917030334,"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/quadratic-unconstrained-binary-optimization","display_name":"Quadratic unconstrained binary optimization","score":0.8298721313476562},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.7061496376991272},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.5930206179618835},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5682443380355835},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5197727084159851},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5091506838798523},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4869926869869232},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4606488049030304},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4501408040523529},{"id":"https://openalex.org/keywords/quantum-annealing","display_name":"Quantum annealing","score":0.43478935956954956},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.4227029085159302},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41731902956962585},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.41460925340652466},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.41085323691368103},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3241714835166931},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3227304518222809},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.14491623640060425},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.13927572965621948},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08095836639404297}],"concepts":[{"id":"https://openalex.org/C177179195","wikidata":"https://www.wikidata.org/wiki/Q7268372","display_name":"Quadratic unconstrained binary optimization","level":4,"score":0.8298721313476562},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.7061496376991272},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5930206179618835},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5682443380355835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5197727084159851},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5091506838798523},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4869926869869232},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4606488049030304},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4501408040523529},{"id":"https://openalex.org/C90408235","wikidata":"https://www.wikidata.org/wiki/Q938141","display_name":"Quantum annealing","level":4,"score":0.43478935956954956},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.4227029085159302},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41731902956962585},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.41460925340652466},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.41085323691368103},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3241714835166931},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3227304518222809},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.14491623640060425},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.13927572965621948},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08095836639404297},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1514581","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1514581","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2335928686","display_name":null,"funder_award_id":"1918549","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8159673325","display_name":null,"funder_award_id":"SAA2-403506","funder_id":"https://openalex.org/F4320306101","funder_display_name":"National Aeronautics and Space Administration"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W1539402525","https://openalex.org/W1967138577","https://openalex.org/W1967344706","https://openalex.org/W1996867747","https://openalex.org/W2005470065","https://openalex.org/W2024860775","https://openalex.org/W2026856626","https://openalex.org/W2028918948","https://openalex.org/W2033040247","https://openalex.org/W2039122980","https://openalex.org/W2070426678","https://openalex.org/W2078600458","https://openalex.org/W2079135578","https://openalex.org/W2106318612","https://openalex.org/W2120146316","https://openalex.org/W2124487034","https://openalex.org/W2132130706","https://openalex.org/W2257937122","https://openalex.org/W2538025098","https://openalex.org/W2564229214","https://openalex.org/W2607116528","https://openalex.org/W2614421097","https://openalex.org/W2771114131","https://openalex.org/W2781738013","https://openalex.org/W2947189577","https://openalex.org/W2955075300","https://openalex.org/W2962853966","https://openalex.org/W2963000054","https://openalex.org/W2963575397","https://openalex.org/W2980708903","https://openalex.org/W3000028936","https://openalex.org/W3005644271","https://openalex.org/W3014405689","https://openalex.org/W3015667706","https://openalex.org/W3035899097","https://openalex.org/W3043792635","https://openalex.org/W3084359136","https://openalex.org/W3098974447","https://openalex.org/W3100931082","https://openalex.org/W3101339117","https://openalex.org/W3102239087","https://openalex.org/W3103832819","https://openalex.org/W3104354927","https://openalex.org/W3109325270","https://openalex.org/W3111162498","https://openalex.org/W3111617275","https://openalex.org/W3124206520","https://openalex.org/W3125232052","https://openalex.org/W3129110052","https://openalex.org/W3165717557","https://openalex.org/W3199543116","https://openalex.org/W3204628099","https://openalex.org/W3210079594","https://openalex.org/W3215405050","https://openalex.org/W4225417080","https://openalex.org/W4248179398","https://openalex.org/W4284976704","https://openalex.org/W4292363360","https://openalex.org/W4319310905"],"related_works":["https://openalex.org/W4380986281","https://openalex.org/W4316012214","https://openalex.org/W2917807404","https://openalex.org/W2893961859","https://openalex.org/W4388555437","https://openalex.org/W2006098914","https://openalex.org/W4287027624","https://openalex.org/W4389168364","https://openalex.org/W4388552999","https://openalex.org/W4380551968"],"abstract_inverted_index":{".Recent":[0],"years":[1],"have":[2],"seen":[3],"significant":[4],"advances":[5],"in":[6,40,65,110],"quantum/quantum-inspired":[7],"technologies":[8,26],"capable":[9],"of":[10,17,23,31,49,96,107,113,129,142,149,162,191,211],"approximately":[11],"searching":[12],"for":[13,181],"the":[14,29,111,140,143,147,154,159,188,209,212,217,221],"ground":[15],"state":[16],"Ising":[18,45,120,222],"spin":[19],"Hamiltonians.":[20],"The":[21],"promise":[22],"leveraging":[24,123],"such":[25],"to":[27,43,60,157,167,197,206],"accelerate":[28],"solution":[30,51,213],"difficult":[32],"optimization":[33,67],"problems":[34,46],"has":[35,89],"spurred":[36],"an":[37,124],"increased":[38],"interest":[39],"exploring":[41],"methods":[42],"integrate":[44],"as":[47,131,133],"part":[48],"their":[50,97],"process,":[52],"with":[53,171],"existing":[54,66,125,178],"approaches":[55,63],"ranging":[56],"from":[57],"direct":[58],"transcription":[59],"hybrid":[61,108,173,193],"quantum-classical":[62,174],"rooted":[64],"algorithms.":[68],"While":[69],"it":[70],"is":[71,195,214],"widely":[72],"acknowledged":[73],"that":[74,187,203],"quantum":[75],"computers":[76],"should":[77],"augment":[78],"classical":[79,189],"computers,":[80],"rather":[81],"than":[82],"replace":[83],"them":[84],"entirely,":[85],"comparatively":[86],"little":[87],"attention":[88],"been":[90],"directed":[91],"toward":[92],"deriving":[93],"analytical":[94],"characterizations":[95],"interactions.":[98],"In":[99],"this":[100,169,192],"paper,":[101],"we":[102,138,185],"present":[103],"a":[104,134,172],"formal":[105],"analysis":[106,161],"algorithms":[109],"context":[112],"solving":[114],"mixed-binary":[115],"quadratic":[116,226],"programs":[117],"(MBQP)":[118],"via":[119],"solvers.":[121],"By":[122],"completely":[126],"positive":[127],"reformulation":[128,156,170],"MBQPs,":[130],"well":[132],"new":[135],"strong-duality":[136],"result,":[137],"show":[139],"exactness":[141],"dual":[144],"problem":[145],"over":[146],"cone":[148],"copositive":[150],"matrices,":[151],"thus":[152],"allowing":[153],"resulting":[155],"inherit":[158],"straightforward":[160],"convex":[163,182],"optimization.":[164],"We":[165],"propose":[166],"solve":[168],"cutting-plane":[175,183],"algorithm.":[176],"Using":[177],"complexity":[179,210],"results":[180],"algorithms,":[184],"deduce":[186],"portion":[190],"framework":[194],"guaranteed":[196],"be":[198],"polynomial":[199],"time.":[200],"This":[201],"suggests":[202],"when":[204],"applied":[205],"NP-hard":[207],"problems,":[208],"shifted":[215],"onto":[216],"subroutine":[218],"handled":[219],"by":[220],"solver.Keywordscopositive":[223],"optimizationIsing":[224],"solversmixed-binary":[225],"programscutting-planeMSC":[227],"codes65K0590C1190C2090C2590C2690C46":[228]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}