{"id":"https://openalex.org/W2318461564","doi":"https://doi.org/10.1112/s1461157000000437","title":"Fast Constructive Recognition of Black-Box Unitary Groups","display_name":"Fast Constructive Recognition of Black-Box Unitary Groups","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2318461564","doi":"https://doi.org/10.1112/s1461157000000437","mag":"2318461564"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157000000437","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000437","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9B505C474D5E0FC9E51CC3633783AEC6/S1461157000000437a.pdf/div-class-title-fast-constructive-recognition-of-black-box-unitary-groups-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9B505C474D5E0FC9E51CC3633783AEC6/S1461157000000437a.pdf/div-class-title-fast-constructive-recognition-of-black-box-unitary-groups-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057832306","display_name":"Peter A. Brooksbank","orcid":"https://orcid.org/0000-0002-3985-2177"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peter A. Brooksbank","raw_affiliation_strings":["Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus OH 43210"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus OH 43210","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057832306"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":0.5516,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.67252637,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"6","issue":null,"first_page":"162","last_page":"197"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9984999895095825,"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/T11797","display_name":"graph theory and CDMA systems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8276206254959106},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.7499626874923706},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6682040095329285},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.6071009635925293},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5675789713859558},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.5662743449211121},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5550567507743835},{"id":"https://openalex.org/keywords/unitary-group","display_name":"Unitary group","score":0.5274931192398071},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.521270751953125},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5148969888687134},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4938574433326721},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4296698570251465},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4072864353656769},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40435653924942017},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3793303370475769},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3500175178050995},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10201853513717651},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09326356649398804},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08944904804229736}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8276206254959106},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7499626874923706},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6682040095329285},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6071009635925293},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5675789713859558},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.5662743449211121},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5550567507743835},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.5274931192398071},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.521270751953125},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5148969888687134},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4938574433326721},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4296698570251465},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4072864353656769},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40435653924942017},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3793303370475769},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3500175178050995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10201853513717651},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09326356649398804},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08944904804229736},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1112/s1461157000000437","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000437","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9B505C474D5E0FC9E51CC3633783AEC6/S1461157000000437a.pdf/div-class-title-fast-constructive-recognition-of-black-box-unitary-groups-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1011.5975","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1011.5975","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Peter_Brooksbank/publication/228422449_Fast_constructive_recognition_of_black-box_unitary_groups/links/5489bc930cf2d1800d7aa04a.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1016.9846","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1016.9846","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.facstaff.bucknell.edu/pbrooksb/docs/Br5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1112/s1461157000000437","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000437","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9B505C474D5E0FC9E51CC3633783AEC6/S1461157000000437a.pdf/div-class-title-fast-constructive-recognition-of-black-box-unitary-groups-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2318461564.pdf","grobid_xml":"https://content.openalex.org/works/W2318461564.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W135053117","https://openalex.org/W171553832","https://openalex.org/W176020141","https://openalex.org/W189760519","https://openalex.org/W618980177","https://openalex.org/W1484687248","https://openalex.org/W1493654001","https://openalex.org/W1854352062","https://openalex.org/W1964582653","https://openalex.org/W1967627221","https://openalex.org/W1969754062","https://openalex.org/W1991451613","https://openalex.org/W2021337234","https://openalex.org/W2033630502","https://openalex.org/W2072053864","https://openalex.org/W2096801475","https://openalex.org/W2103998840","https://openalex.org/W2113555467","https://openalex.org/W2184608745","https://openalex.org/W2338560738","https://openalex.org/W2398949003","https://openalex.org/W4230845625","https://openalex.org/W4242259951","https://openalex.org/W6642354590","https://openalex.org/W6675455766","https://openalex.org/W6676699027"],"related_works":["https://openalex.org/W1555245969","https://openalex.org/W2321282558","https://openalex.org/W2299507895","https://openalex.org/W1900540279","https://openalex.org/W2944491272","https://openalex.org/W4300498183","https://openalex.org/W2577600644","https://openalex.org/W1866724006","https://openalex.org/W2012392278","https://openalex.org/W2656095712"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"the":[4,23,43],"author":[5],"presents":[6],"a":[7,14,19],"new":[8],"algorithm":[9,37],"to":[10],"recognise,":[11],"constructively,":[12],"when":[13],"given":[15],"black-box":[16],"group":[17,25],"is":[18],"homomorphic":[20],"image":[21],"of":[22,45,61],"unitary":[24],"SU(":[26],"d,":[27],"q":[28,34,50,63],")":[29,51],"for":[30,47,54],"known":[31],"d":[32],"and":[33,53],".":[35],"The":[36],"runs":[38],"in":[39,58],"polynomial":[40],"time,":[41],"assuming":[42],"existence":[44],"oracles":[46],"handling":[48],"SL(2,":[49],"subgroups,":[52],"computing":[55],"discrete":[56],"logarithms":[57],"cyclic":[59],"groups":[60],"order":[62],"\u00b1":[64],"1.":[65]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
