{"id":"https://openalex.org/W2035627701","doi":"https://doi.org/10.1137/050643684","title":"Quantum Algorithms for the Triangle Problem","display_name":"Quantum Algorithms for the Triangle Problem","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2035627701","doi":"https://doi.org/10.1137/050643684","mag":"2035627701"},"language":"en","primary_location":{"id":"doi:10.1137/050643684","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050643684","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5045780938","display_name":"Fr\u00e9d\u00e9ric Magniez","orcid":"https://orcid.org/0000-0003-2384-9026"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Magniez","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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miklos Santha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113860564","display_name":"M\u00e1ri\u00f3 Szegedy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mario Szegedy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.9852,"has_fulltext":false,"cited_by_count":323,"citation_normalized_percentile":{"value":0.99030887,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"37","issue":"2","first_page":"413","last_page":"424"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9804999828338623,"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"}},{"id":"https://openalex.org/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9778000116348267,"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/quantum-algorithm","display_name":"Quantum algorithm","score":0.6059440970420837},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.59535813331604},{"id":"https://openalex.org/keywords/subroutine","display_name":"Subroutine","score":0.5395770072937012},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5302972793579102},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5141156315803528},{"id":"https://openalex.org/keywords/quantum-walk","display_name":"Quantum walk","score":0.49695828557014465},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.4701633155345917},{"id":"https://openalex.org/keywords/search-algorithm","display_name":"Search algorithm","score":0.43313759565353394},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4330673813819885},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4279625713825226},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4196017384529114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.301444411277771},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11406129598617554},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10814735293388367}],"concepts":[{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.6059440970420837},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.59535813331604},{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.5395770072937012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5302972793579102},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5141156315803528},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.49695828557014465},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.4701633155345917},{"id":"https://openalex.org/C125583679","wikidata":"https://www.wikidata.org/wiki/Q755673","display_name":"Search algorithm","level":2,"score":0.43313759565353394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4330673813819885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4279625713825226},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4196017384529114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.301444411277771},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11406129598617554},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10814735293388367},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050643684","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050643684","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1872909421","https://openalex.org/W1967066104","https://openalex.org/W1993000433","https://openalex.org/W2016606569","https://openalex.org/W2034038586","https://openalex.org/W2044747430","https://openalex.org/W2050334794","https://openalex.org/W2101724873","https://openalex.org/W2117584890","https://openalex.org/W2122780600","https://openalex.org/W2126323053","https://openalex.org/W2146111707","https://openalex.org/W2147862220","https://openalex.org/W2148132004","https://openalex.org/W3041308142"],"related_works":["https://openalex.org/W2089342336","https://openalex.org/W2949694831","https://openalex.org/W3114654323","https://openalex.org/W1968287309","https://openalex.org/W2883913628","https://openalex.org/W2800432156","https://openalex.org/W1566596544","https://openalex.org/W638834885","https://openalex.org/W4320736706","https://openalex.org/W2025956887"],"abstract_inverted_index":{"We":[0],"present":[1],"two":[2],"new":[3],"quantum":[4,78,109],"algorithms":[5],"that":[6,73],"either":[7],"find":[8],"a":[9,53],"triangle":[10,28],"(a":[11],"copy":[12],"of":[13,56,60,67,77,87,94,150,152],"$K_{3}$)":[14],"in":[15,85,107,124],"an":[16,137],"undirected":[17],"graph":[18],"G":[19,26],"on":[20,52,65,92],"n":[21],"nodes,":[22],"or":[23],"reject":[24],"if":[25],"is":[27,50,147],"free.":[29],"The":[30,43,99,118],"first":[31,100,122],"algorithm":[32,45,101,138],"uses":[33,46,102,115],"combinatorial":[34],"ideas":[35],"with":[36,139],"Grover":[37,81],"Search":[38,82],"and":[39,49],"makes":[40],"$\\tilde{O}(n^{10/7})$":[41],"queries.":[42],"second":[44,113],"$\\tilde{O}(n^{13/10})$":[47],"queries":[48],"based":[51],"design":[54],"concept":[55],"Ambainis":[57],"[in":[58],"Proceedings":[59,86],"the":[61,75,88,112,148],"$45$th":[62],"IEEE":[63],"Symposium":[64,91],"Foundations":[66],"Computer":[68],"Science,":[69],"2004,":[70],"pp.":[71,97,134],"22\u201331]":[72],"incorporates":[74],"benefits":[76],"walks":[79],"into":[80],"[L.":[83],"Grover,":[84],"Twenty\u2010Eighth":[89],"ACM":[90],"Theory":[93],"Computing,":[95],"1996,":[96],"212\u2013219].":[98],"only":[103],"$O(\\log":[104],"n)$":[105],"qubits":[106],"its":[108],"subroutines,":[110],"whereas":[111],"one":[114],"$O(n)$":[116],"qubits.":[117],"Triangle":[119],"Problem":[120],"was":[121,143],"treated":[123],"[H.":[125],"Buhrman":[126],"et":[127],"al.,":[128],"SIAM":[129],"J.":[130],"Comput.,":[131],"34":[132],"(2005),":[133],"1324\u20131330],":[135],"where":[136,145],"$O(n+\\sqrt{nm})$":[140],"query":[141],"complexity":[142],"presented,":[144],"m":[146],"number":[149],"edges":[151],"G.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":20},{"year":2021,"cited_by_count":24},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":18},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":19}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
