{"id":"https://openalex.org/W2031374990","doi":"https://doi.org/10.1137/080712167","title":"Any AND-OR Formula of Size <i>N</i> Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer","display_name":"Any AND-OR Formula of Size <i>N</i> Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2031374990","doi":"https://doi.org/10.1137/080712167","mag":"2031374990"},"language":"en","primary_location":{"id":"doi:10.1137/080712167","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080712167","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/A5045669197","display_name":"Andris Ambainis","orcid":"https://orcid.org/0000-0002-8716-001X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. Ambainis","raw_affiliation_strings":["ambainis@lu.lv#TAB#"],"affiliations":[{"raw_affiliation_string":"ambainis@lu.lv#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018837979","display_name":"Andrew M. Childs","orcid":"https://orcid.org/0000-0002-9903-837X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. M. Childs","raw_affiliation_strings":["amchilds@uwaterloo.ca#TAB#"],"affiliations":[{"raw_affiliation_string":"amchilds@uwaterloo.ca#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065994445","display_name":"Ben W. Reichardt","orcid":"https://orcid.org/0000-0002-4934-8732"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. W. Reichardt","raw_affiliation_strings":["breic@uwaterloo.ca#TAB#"],"affiliations":[{"raw_affiliation_string":"breic@uwaterloo.ca#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048758282","display_name":"Robert \u0160palek","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. \u0160palek","raw_affiliation_strings":["spalek@google.com#TAB#"],"affiliations":[{"raw_affiliation_string":"spalek@google.com#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080912671","display_name":"S. Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Zhang","raw_affiliation_strings":["syzhang@cse.cuhk.edu.hk#TAB#"],"affiliations":[{"raw_affiliation_string":"syzhang@cse.cuhk.edu.hk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5045669197"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.7929,"has_fulltext":false,"cited_by_count":122,"citation_normalized_percentile":{"value":0.99081198,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"39","issue":"6","first_page":"2513","last_page":"2530"},"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9936000108718872,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9919999837875366,"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/bounded-function","display_name":"Bounded function","score":0.6506268382072449},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5942061543464661},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5709262490272522},{"id":"https://openalex.org/keywords/quantum-phase-estimation-algorithm","display_name":"Quantum phase estimation algorithm","score":0.5553469061851501},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.542917013168335},{"id":"https://openalex.org/keywords/quantum-walk","display_name":"Quantum walk","score":0.526655912399292},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.46614590287208557},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.44567254185676575},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.4400831460952759},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4371604919433594},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40159133076667786},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.2138977348804474},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17069679498672485},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16280877590179443},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13225024938583374},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09227058291435242}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6506268382072449},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5942061543464661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5709262490272522},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.5553469061851501},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.542917013168335},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.526655912399292},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.46614590287208557},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.44567254185676575},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4400831460952759},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4371604919433594},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40159133076667786},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.2138977348804474},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17069679498672485},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16280877590179443},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13225024938583374},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09227058291435242}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/080712167","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080712167","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":14,"referenced_works":["https://openalex.org/W1517311456","https://openalex.org/W1987152249","https://openalex.org/W2002372750","https://openalex.org/W2009269558","https://openalex.org/W2009353303","https://openalex.org/W2026325622","https://openalex.org/W2069796292","https://openalex.org/W2099170023","https://openalex.org/W2109741106","https://openalex.org/W2110503949","https://openalex.org/W2120560473","https://openalex.org/W2122780600","https://openalex.org/W2123056342","https://openalex.org/W2126323053"],"related_works":["https://openalex.org/W3127020915","https://openalex.org/W1968287309","https://openalex.org/W4385007402","https://openalex.org/W2751437615","https://openalex.org/W2009948449","https://openalex.org/W3194478582","https://openalex.org/W3092769055","https://openalex.org/W1493399357","https://openalex.org/W3015365583","https://openalex.org/W4385681739"],"abstract_inverted_index":{"Consider":[0],"the":[1,43,62,65],"problem":[2,22],"of":[3,42,64],"evaluating":[4],"an":[5,9],"AND-OR":[6],"formula":[7],"on":[8,55],"N-bit":[10],"black-box":[11],"input.":[12],"We":[13],"present":[14],"a":[15,51,56],"bounded-error":[16],"quantum":[17,53],"algorithm":[18,44],"that":[19],"solves":[20],"this":[21],"in":[23,34],"time":[24],"$N^{1/2+o(1)}$.":[25],"In":[26],"particular,":[27],"approximately":[28],"balanced":[29],"formulas":[30],"can":[31],"be":[32],"evaluated":[33],"$O(\\sqrt{N})$":[35],"queries,":[36],"which":[37],"is":[38,45],"optimal.":[39],"The":[40],"idea":[41],"to":[46,50],"apply":[47],"phase":[48],"estimation":[49],"discrete-time":[52],"walk":[54],"weighted":[57],"tree":[58],"whose":[59],"spectrum":[60],"encodes":[61],"value":[63],"formula.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
