{"id":"https://openalex.org/W2962782131","doi":"https://doi.org/10.4086/toc.2018.v014a001","title":"","display_name":"","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2962782131","doi":"https://doi.org/10.4086/toc.2018.v014a001","mag":"2962782131"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2018.v014a001","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2018.v014a001","pdf_url":"http://www.theoryofcomputing.org/articles/v014a001/v014a001.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.theoryofcomputing.org/articles/v014a001/v014a001.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010322438","display_name":"Itai Arad","orcid":"https://orcid.org/0009-0005-5481-6333"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Itai Arad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046562790","display_name":"Mikl\u00f3s S\u00e1ntha","orcid":null},"institutions":[{"id":"https://openalex.org/I115455960","display_name":"Centre for Quantum Technologies","ror":"https://ror.org/01mgdzc49","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115455960"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR","SG"],"is_corresponding":false,"raw_author_name":"Miklos Santha","raw_affiliation_strings":["CQT - Centre for Quantum Technologies [Singapore] (Block S15, 3 Science Drive 2, Singapour 117543 - Singapore)","IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13 - France)","CNRS - Centre National de la Recherche Scientifique (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CQT - Centre for Quantum Technologies [Singapore] (Block S15, 3 Science Drive 2, Singapour 117543 - Singapore)","institution_ids":["https://openalex.org/I115455960"]},{"raw_affiliation_string":"IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13 - France)","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210117673"]},{"raw_affiliation_string":"CNRS - Centre National de la Recherche Scientifique (France)","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075780348","display_name":"Aarthi Sundaram","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aarthi Sundaram","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100757082","display_name":"Shengyu Zhang","orcid":"https://orcid.org/0000-0001-5907-2277"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shengyu Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5602,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.78049209,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"1","first_page":"1","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9864000082015991,"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":0.9864000082015991,"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/T10126","display_name":"Logic, programming, and type systems","score":0.984499990940094,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9794999957084656,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.6874918937683105},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.605010986328125},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5808566808700562},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5784816741943359},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5391886830329895},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5265771746635437},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4794853627681732},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47776520252227783},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.45475494861602783},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.44581225514411926},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4126773774623871},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3909812271595001},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.24476298689842224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2416333556175232},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11498558521270752}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6874918937683105},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.605010986328125},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5808566808700562},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5784816741943359},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5391886830329895},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5265771746635437},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4794853627681732},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47776520252227783},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.45475494861602783},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.44581225514411926},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4126773774623871},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3909812271595001},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.24476298689842224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2416333556175232},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11498558521270752},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4086/toc.2018.v014a001","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2018.v014a001","pdf_url":"http://www.theoryofcomputing.org/articles/v014a001/v014a001.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02350768v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02350768","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Theory of Computing Systems, 2018, 14 (1), pp.1-27. &#x27E8;10.4086/toc.2018.v014a001&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.4086/toc.2018.v014a001","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2018.v014a001","pdf_url":"http://www.theoryofcomputing.org/articles/v014a001/v014a001.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2436444117","display_name":null,"funder_award_id":"ANR-12-BS02-005","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3261977963","display_name":"Quantum Algorithmics","funder_award_id":"600700","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6437558859","display_name":null,"funder_award_id":"MOE2012-T3-1-009","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G6702880738","display_name":null,"funder_award_id":"ANR-12","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G731534506","display_name":"Magma chamber to micro-habitats : dynamics of deep sea hydrothermal ecosystems","funder_award_id":"ANR-14-CE02-0008","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7439166332","display_name":null,"funder_award_id":"ANR-12-BS02-005","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7712274940","display_name":null,"funder_award_id":"MOE2012-T3-1-009","funder_id":"https://openalex.org/F4320324089","funder_display_name":"Centre for Quantum Technologies"},{"id":"https://openalex.org/G8717141228","display_name":"Algorithmic Techniques for Restricted Data Access Models","funder_award_id":"ANR-12-BS02-0005","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"},{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"},{"id":"https://openalex.org/F4320324089","display_name":"Centre for Quantum Technologies","ror":"https://ror.org/01mgdzc49"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2962782131.pdf","grobid_xml":"https://content.openalex.org/works/W2962782131.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1496801598","https://openalex.org/W1754110195","https://openalex.org/W1820801893","https://openalex.org/W1896347490","https://openalex.org/W1922629554","https://openalex.org/W1975727776","https://openalex.org/W1990516747","https://openalex.org/W2003160050","https://openalex.org/W2031823362","https://openalex.org/W2034920898","https://openalex.org/W2036265926","https://openalex.org/W2057361103","https://openalex.org/W2062897452","https://openalex.org/W2077925882","https://openalex.org/W2084019889","https://openalex.org/W2135273380","https://openalex.org/W2144126354","https://openalex.org/W2286510190","https://openalex.org/W2296189723","https://openalex.org/W2401610261","https://openalex.org/W2554893608","https://openalex.org/W2887977568","https://openalex.org/W2963378030","https://openalex.org/W2994777601","https://openalex.org/W4226347946"],"related_works":["https://openalex.org/W2134613344","https://openalex.org/W2409877639","https://openalex.org/W4388704119","https://openalex.org/W2910123824","https://openalex.org/W4213379151","https://openalex.org/W3206120658","https://openalex.org/W1889203613","https://openalex.org/W4281550036","https://openalex.org/W2035510778","https://openalex.org/W2766195849"],"abstract_inverted_index":{"A":[0],"well-known":[1],"result":[2],"about":[3],"satisfiability":[4],"theory":[5],"is":[6,48,74,90,160,185,222],"that":[7,125,198,203],"the":[8,18,21,25,46,52,81,86,94,126,140,161,174,186,193,206,216,229],"2-SAT":[9,27,83,128],"problem":[10,73,84,95,129],"can":[11,152],"be":[12,153],"solved":[13],"in":[14,117,139,155,173,197,205],"linear":[15],"time,":[16,157],"despite":[17],"NP-hardness":[19],"of":[20,34,42,80,96,101,105,134,143,163,188,219,231],"3-SAT":[22],"problem.":[23],"In":[24,165],"quantum":[26,87,127],"problem,":[28],"we":[29,168],"are":[30,64],"given":[31],"a":[32,40,59,77,98,108,131,170,211],"family":[33],"2-qubit":[35],"projectors":[36],"i":[37,56],"j":[38,57],"on":[39,149],"system":[41],"n":[43,159],"qubits,":[44],"and":[45,158],"task":[47],"to":[49,85,93,112],"decide":[50],"whether":[51],"Hamiltonian":[53],"H":[54],"=":[55,70],"has":[58,123,130,210],"0-eigenvalue,":[60],"or":[61],"all":[62],"eigenvalues":[63],"greater":[65],"than":[66],"1/n":[67],"for":[68],"some":[69],"O(1).":[71],"The":[72],"not":[75],"only":[76],"natural":[78],"extension":[79],"classical":[82],"case,":[88],"but":[89],"also":[91,201],"equivalent":[92],"finding":[97],"ground":[99],"state":[100],"2-local":[102],"frustration-free":[103],"Hamiltonians":[104],"spin":[106],"1/2,":[107],"well-studied":[109],"model":[110,142,176],"believed":[111],"capture":[113],"certain":[114],"key":[115],"properties":[116],"modern":[118],"condensed":[119],"matter":[120],"physics.":[121],"Bravyi":[122],"shown":[124],"deterministic":[132,171],"algorithm":[133,172,221],"complexity":[135,196,218,230],"O(n":[136,180],"4":[137],")":[138],"algebraic":[141,175],"computation":[144],"where":[145,183,226],"every":[146,208],"arithmetic":[147],"operation":[148],"complex":[150],"numbers":[151],"performed":[154],"unit":[156],"number":[162,187,209],"variables.":[164],"this":[166],"paper":[167],"give":[169],"with":[177],"running":[178],"time":[179],"+":[181,224],"m),":[182],"m":[184],"local":[189],"projectors,":[190],"therefore":[191],"achieving":[192],"best":[194],"possible":[195],"model.":[199],"We":[200],"show":[202],"if":[204],"input":[207],"constant":[212],"size":[213],"representation":[214],"then":[215],"bit":[217],"our":[220],"O((n":[223],"m)M(n)),":[225],"M(n)":[227],"denotes":[228],"multiplying":[232],"two":[233],"n-bit":[234],"integers.":[235]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-26T07:53:14.480251","created_date":"2019-07-30T00:00:00"}
