{"id":"https://openalex.org/W2147548586","doi":"https://doi.org/10.26421/qic9.3-4-3","title":"Efficient quantum algorithm for identifying hidden polynomials","display_name":"Efficient quantum algorithm for identifying hidden polynomials","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2147548586","doi":"https://doi.org/10.26421/qic9.3-4-3","mag":"2147548586"},"language":"en","primary_location":{"id":"doi:10.26421/qic9.3-4-3","is_oa":false,"landing_page_url":"https://doi.org/10.26421/qic9.3-4-3","pdf_url":null,"source":{"id":"https://openalex.org/S41034432","display_name":"Quantum Information and Computation","issn_l":"1533-7146","issn":["1533-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322612","host_organization_name":"Rinton Press","host_organization_lineage":["https://openalex.org/P4310322612"],"host_organization_lineage_names":["Rinton Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://stars.library.ucf.edu/scopus2000/12024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042463876","display_name":"Thomas Decker","orcid":"https://orcid.org/0000-0001-9683-0620"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"T. Decker","raw_affiliation_strings":["School of Computer Science, McGill University Montr\u00e9al, Qu\u00e9bec, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, McGill University Montr\u00e9al, Qu\u00e9bec, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084270459","display_name":"Jan Draisma","orcid":"https://orcid.org/0000-0001-7248-8250"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]},{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"J. Draisma","raw_affiliation_strings":["Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, The Netherlands and Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, The Netherlands and Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands#TAB#","institution_ids":["https://openalex.org/I1341640284","https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091077518","display_name":"Pawe\u0142 Wocjan","orcid":null},"institutions":[{"id":"https://openalex.org/I106165777","display_name":"University of Central Florida","ror":"https://ror.org/036nfer12","country_code":"US","type":"education","lineage":["https://openalex.org/I106165777"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. Wocjan","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL","institution_ids":["https://openalex.org/I106165777"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042463876"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":3.1614,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.92452333,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"3&4","first_page":"215","last_page":"230"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9980000257492065,"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/mathematics","display_name":"Mathematics","score":0.7409466505050659},{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.7089644074440002},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5690340399742126},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5445868968963623},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5339573621749878},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5182018876075745},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4924112558364868},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4881909489631653},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.479744553565979},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4778677821159363},{"id":"https://openalex.org/keywords/random-variate","display_name":"Random variate","score":0.42156484723091125},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.33088070154190063},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.3078983426094055},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11106902360916138}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7409466505050659},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.7089644074440002},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5690340399742126},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5445868968963623},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5339573621749878},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5182018876075745},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4924112558364868},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4881909489631653},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.479744553565979},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4778677821159363},{"id":"https://openalex.org/C141547133","wikidata":"https://www.wikidata.org/wiki/Q7291996","display_name":"Random variate","level":3,"score":0.42156484723091125},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.33088070154190063},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3078983426094055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11106902360916138},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.26421/qic9.3-4-3","is_oa":false,"landing_page_url":"https://doi.org/10.26421/qic9.3-4-3","pdf_url":null,"source":{"id":"https://openalex.org/S41034432","display_name":"Quantum Information and Computation","issn_l":"1533-7146","issn":["1533-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322612","host_organization_name":"Rinton Press","host_organization_lineage":["https://openalex.org/P4310322612"],"host_organization_lineage_names":["Rinton Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information and Computation","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/656dde85-48f1-417b-af8d-95dc7cc83458","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/656dde85-48f1-417b-af8d-95dc7cc83458","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Decker, T, Draisma, J & Wocjan, P 2009, 'Efficient quantum algorithm for identifying hidden polynomials', Quantum Information and Computation, vol. 9, no. 3-4, pp. 215-230.","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.tue.nl:publications/04fdc3f7-3843-472f-aa36-b7f3229fabce","is_oa":false,"landing_page_url":"http://arxiv.org/pdf/0706.1219","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Decker , T , Draisma , J & Wocjan , P 2007 , Efficient quantum algorithm for identifying hidden polynomials . arXiv.org [quant-ph] , vol. 0706.1219 , s.n.","raw_type":"book"},{"id":"pmh:oai:stars.library.ucf.edu:scopus2000-13023","is_oa":true,"landing_page_url":"https://stars.library.ucf.edu/scopus2000/12024","pdf_url":null,"source":{"id":"https://openalex.org/S4210172555","display_name":"Journal of International Crisis and Risk Communication Research","issn_l":"2576-0017","issn":["2576-0017","2576-0025"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus Export 2000s","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.250.1962","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.1962","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0706.1219v2.pdf","raw_type":"text"},{"id":"pmh:oai:library.tue.nl:649869","is_oa":false,"landing_page_url":"http://repository.tue.nl/649869","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1533-7146","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/04fdc3f7-3843-472f-aa36-b7f3229fabce","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/04fdc3f7-3843-472f-aa36-b7f3229fabce","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Decker , T , Draisma , J & Wocjan , P 2007 , Efficient quantum algorithm for identifying hidden polynomials . arXiv.org [quant-ph] , vol. 0706.1219 , s.n.","raw_type":"book"},{"id":"pmh:tue:oai:pure.tue.nl:publications/04fdc3f7-3843-472f-aa36-b7f3229fabce","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/04fdc3f7-3843-472f-aa36-b7f3229fabce","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:tue:oai:pure.tue.nl:publications/656dde85-48f1-417b-af8d-95dc7cc83458","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/656dde85-48f1-417b-af8d-95dc7cc83458","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum Information & Computation, 9(3-4), 215 - 230. Rinton Press Inc.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:stars.library.ucf.edu:scopus2000-13023","is_oa":true,"landing_page_url":"https://stars.library.ucf.edu/scopus2000/12024","pdf_url":null,"source":{"id":"https://openalex.org/S4210172555","display_name":"Journal of International Crisis and Risk Communication Research","issn_l":"2576-0017","issn":["2576-0017","2576-0025"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus Export 2000s","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W64656188","https://openalex.org/W205639526","https://openalex.org/W1487721777","https://openalex.org/W1497005608","https://openalex.org/W1498202005","https://openalex.org/W1518341038","https://openalex.org/W1535463230","https://openalex.org/W1562183207","https://openalex.org/W1579192564","https://openalex.org/W1587133324","https://openalex.org/W1671272902","https://openalex.org/W1996143071","https://openalex.org/W2005536816","https://openalex.org/W2009106180","https://openalex.org/W2017112356","https://openalex.org/W2038714372","https://openalex.org/W2060509762","https://openalex.org/W2066153786","https://openalex.org/W2066284946","https://openalex.org/W2090330739","https://openalex.org/W2131378873","https://openalex.org/W2140496956","https://openalex.org/W2171389569","https://openalex.org/W2962824714","https://openalex.org/W3043060850","https://openalex.org/W3111297213"],"related_works":["https://openalex.org/W2388953866","https://openalex.org/W2349918401","https://openalex.org/W1963889177","https://openalex.org/W2362355910","https://openalex.org/W4254888883","https://openalex.org/W2784077364","https://openalex.org/W2126856880","https://openalex.org/W2092976320","https://openalex.org/W2953274551","https://openalex.org/W2030775750"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,24,78,89,97,109,122],"natural":[3],"generalization":[4],"of":[5,20,34,51,58,63,112,114],"an":[6],"abelian":[7],"Hidden":[8],"Subgroup":[9],"Problem":[10],"where":[11],"the":[12,35],"subgroups":[13],"and":[14,73,119],"their":[15],"cosets":[16],"correspond":[17],"to":[18,41,68,87],"graphs":[19],"linear":[21,43],"functions":[22,33,50],"over":[23],"finite":[25,110],"field":[26],"$\\F$":[27],"with":[28,116],"$d$":[29,115],"elements.":[30],"The":[31,56],"hidden":[32,60,104],"generalized":[36],"problem":[37,57],"are":[38,85],"not":[39],"restricted":[40],"be":[42,47],"but":[44,108],"can":[45],"also":[46],"$m$-variate":[48,61],"polynomial":[49],"total":[52],"degree":[53,64],"$n\\geq":[54],"2$.":[55],"identifying":[59],"polynomials":[62,105],"less":[65],"or":[66],"equal":[67],"$n$":[69,72],"for":[70,106],"fixed":[71],"$m$":[74],"is":[75,126],"hard":[76],"on":[77],"classical":[79],"computer":[80],"since":[81],"$\\Omega(\\sqrt{d})$":[82],"black-box":[83],"queries":[84],"required":[86],"guarantee":[88],"constant":[90,117],"success":[91],"probability.":[92],"In":[93],"contrast,":[94],"we":[95],"present":[96],"quantum":[98],"algorithm":[99],"that":[100,120,125],"correctly":[101],"identifies":[102],"such":[103],"all":[107],"number":[111],"values":[113],"probability":[118],"has":[121],"running":[123],"time":[124],"only":[127],"polylogarithmic":[128],"in":[129],"$d$.":[130]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}