{"id":"https://openalex.org/W2030937251","doi":"https://doi.org/10.1145/1198513.1198525","title":"Generic quantum Fourier transforms","display_name":"Generic quantum Fourier transforms","publication_year":2006,"publication_date":"2006-10-01","ids":{"openalex":"https://openalex.org/W2030937251","doi":"https://doi.org/10.1145/1198513.1198525","mag":"2030937251"},"language":"en","primary_location":{"id":"doi:10.1145/1198513.1198525","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1198513.1198525","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","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/A5008033989","display_name":"Cristopher Moore","orcid":"https://orcid.org/0000-0002-2062-1942"},"institutions":[{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]},{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cristopher Moore","raw_affiliation_strings":["University of New Mexico and the Santa Fe Institute, Albuquerque, NM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of New Mexico and the Santa Fe Institute, Albuquerque, NM","institution_ids":["https://openalex.org/I1308548392","https://openalex.org/I169521973"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072455364","display_name":"Daniel N. Rockmore","orcid":"https://orcid.org/0000-0001-5411-9224"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]},{"id":"https://openalex.org/I4210166639","display_name":"Dartmouth Hospital","ror":"https://ror.org/02j3qj605","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I4210166639"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Daniel Rockmore","raw_affiliation_strings":["Dartmouth College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dartmouth College","institution_ids":["https://openalex.org/I107672454","https://openalex.org/I4210166639"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088846595","display_name":"Alexander Russell","orcid":"https://orcid.org/0000-0002-8228-6238"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander Russell","raw_affiliation_strings":["University of Connecticut"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Connecticut","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9265,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.93488143,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2","issue":"4","first_page":"707","last_page":"723"},"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9965999722480774,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6874215602874756},{"id":"https://openalex.org/keywords/quantum-fourier-transform","display_name":"Quantum Fourier transform","score":0.6217432022094727},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5984879732131958},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5650224089622498},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5619227290153503},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5308718681335449},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5196227431297302},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.48142167925834656},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.4272860884666443},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39416590332984924},{"id":"https://openalex.org/keywords/quantum-gate","display_name":"Quantum gate","score":0.23401513695716858},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17519217729568481},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15752169489860535},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09797170758247375}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6874215602874756},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.6217432022094727},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5984879732131958},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5650224089622498},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5619227290153503},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5308718681335449},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5196227431297302},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.48142167925834656},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4272860884666443},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39416590332984924},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.23401513695716858},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17519217729568481},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15752169489860535},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09797170758247375}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1198513.1198525","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1198513.1198525","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1488323463","https://openalex.org/W1529069840","https://openalex.org/W1578920057","https://openalex.org/W1596185498","https://openalex.org/W1608473410","https://openalex.org/W1632987656","https://openalex.org/W1964153492","https://openalex.org/W1967088292","https://openalex.org/W1971407031","https://openalex.org/W1986263670","https://openalex.org/W2032830293","https://openalex.org/W2049320929","https://openalex.org/W2055201875","https://openalex.org/W2059004945","https://openalex.org/W2061171222","https://openalex.org/W2061578137","https://openalex.org/W2078992516","https://openalex.org/W2092852220","https://openalex.org/W2097358487","https://openalex.org/W2102008187","https://openalex.org/W2126166880","https://openalex.org/W2143677375","https://openalex.org/W2156190205","https://openalex.org/W2322808352","https://openalex.org/W2799004609","https://openalex.org/W2911959663","https://openalex.org/W3023478445","https://openalex.org/W3111297213","https://openalex.org/W3159676034","https://openalex.org/W4213214460","https://openalex.org/W6634682466"],"related_works":["https://openalex.org/W3101872593","https://openalex.org/W2953274551","https://openalex.org/W2313831037","https://openalex.org/W2335554641","https://openalex.org/W2962738101","https://openalex.org/W1675170525","https://openalex.org/W2250611988","https://openalex.org/W2004326050","https://openalex.org/W2136257094","https://openalex.org/W1617762673"],"abstract_inverted_index":{"The":[0],"quantum":[1,13,25,65,105],"Fourier":[2,45],"transform":[3],"(QFT)":[4],"is":[5],"a":[6,17,71],"principal":[7],"ingredient":[8],"appearing":[9],"in":[10],"many":[11,93],"efficient":[12,24,43,64,87],"algorithms.":[14],"We":[15],"present":[16],"generic":[18],"framework":[19],"for":[20,27,39,67,85,107,131],"the":[21,28,32,40,68,102,108,111,125],"construction":[22,41],"of":[23,36,42,58,74,83,128],"circuits":[26,66,106],"QFT":[29,69,109],"by":[30],"\u201cquantizing\u201d":[31],"highly":[33],"successful":[34],"separation":[35],"variables":[37],"technique":[38],"classical":[44],"transforms.":[46],"Specifically,":[47],"we":[48],"apply":[49],"Bratteli":[50],"diagrams,":[51],"Gel'fand-Tsetlin":[52],"bases,":[53],"and":[54,77,92,124],"strong":[55],"generating":[56],"sets":[57],"small":[59],"adapted":[60],"diameter":[61],"to":[62],"provide":[63],"over":[70,110],"wide":[72],"variety":[73],"finite":[75,126],"Abelian":[76],"non-Abelian":[78],"groups,":[79],"including":[80],"all":[81],"families":[82,95],"groups":[84,113,127],"which":[86],"QFTs":[88],"are":[89],"currently":[90],"known":[91],"new":[94],"as":[96],"well.":[97],"Moreover,":[98],"our":[99],"method":[100],"provides":[101],"first":[103],"subexponential-size":[104],"linear":[112],"GL":[114],"k":[115,120],"(":[116,121],"q":[117,122,136],"),":[118,123],"SL":[119],"Lie":[129],"type,":[130],"any":[132],"fixed":[133],"prime":[134],"power":[135],".":[137]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
