{"id":"https://openalex.org/W3010036675","doi":"https://doi.org/10.1002/nla.2331","title":"Quantum Fourier transform revisited","display_name":"Quantum Fourier transform revisited","publication_year":2020,"publication_date":"2020-09-15","ids":{"openalex":"https://openalex.org/W3010036675","doi":"https://doi.org/10.1002/nla.2331","mag":"3010036675"},"language":"en","primary_location":{"id":"doi:10.1002/nla.2331","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.2331","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.03011","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Daan Camps","orcid":"https://orcid.org/0000-0003-0236-4353"},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daan Camps","raw_affiliation_strings":["Computational Research Division Lawrence Berkeley National Laboratory  Berkeley California USA"],"raw_orcid":"https://orcid.org/0000-0003-0236-4353","affiliations":[{"raw_affiliation_string":"Computational Research Division Lawrence Berkeley National Laboratory  Berkeley California USA","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Roel Van Beeumen","orcid":"https://orcid.org/0000-0003-2276-1153"},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Roel Van Beeumen","raw_affiliation_strings":["Computational Research Division Lawrence Berkeley National Laboratory  Berkeley California USA"],"raw_orcid":"https://orcid.org/0000-0003-2276-1153","affiliations":[{"raw_affiliation_string":"Computational Research Division Lawrence Berkeley National Laboratory  Berkeley California USA","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"last","author":{"id":null,"display_name":"Chao Yang","orcid":"https://orcid.org/0000-0001-7172-7539"},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chao Yang","raw_affiliation_strings":["Computational Research Division Lawrence Berkeley National Laboratory  Berkeley California USA"],"raw_orcid":"https://orcid.org/0000-0001-7172-7539","affiliations":[{"raw_affiliation_string":"Computational Research Division Lawrence Berkeley National Laboratory  Berkeley California USA","institution_ids":["https://openalex.org/I148283060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I148283060"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":1.3589,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.84995001,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"28","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9243000149726868,"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":0.9243000149726868,"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/T12303","display_name":"Tensor decomposition and applications","score":0.011900000274181366,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11804","display_name":"Quantum many-body systems","score":0.004699999932199717,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-fourier-transform","display_name":"Quantum Fourier transform","score":0.828499972820282},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.6528000235557556},{"id":"https://openalex.org/keywords/kronecker-product","display_name":"Kronecker product","score":0.6194000244140625},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.5963000059127808},{"id":"https://openalex.org/keywords/dft-matrix","display_name":"DFT matrix","score":0.579200029373169},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.578000009059906},{"id":"https://openalex.org/keywords/quantum-phase-estimation-algorithm","display_name":"Quantum phase estimation algorithm","score":0.5752999782562256},{"id":"https://openalex.org/keywords/prime-factor-fft-algorithm","display_name":"Prime-factor FFT algorithm","score":0.5156999826431274},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.5040000081062317},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4821000099182129}],"concepts":[{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.828499972820282},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.6528000235557556},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.6194000244140625},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5963000059127808},{"id":"https://openalex.org/C103945485","wikidata":"https://www.wikidata.org/wiki/Q5204933","display_name":"DFT matrix","level":5,"score":0.579200029373169},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.578000009059906},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.5752999782562256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5515999794006348},{"id":"https://openalex.org/C77928272","wikidata":"https://www.wikidata.org/wiki/Q7243214","display_name":"Prime-factor FFT algorithm","level":5,"score":0.5156999826431274},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.5040000081062317},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4821000099182129},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.4569000005722046},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45320001244544983},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.453000009059906},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.44119998812675476},{"id":"https://openalex.org/C43060483","wikidata":"https://www.wikidata.org/wiki/Q17006372","display_name":"Cyclotomic fast Fourier transform","level":5,"score":0.4025000035762787},{"id":"https://openalex.org/C103755468","wikidata":"https://www.wikidata.org/wiki/Q17103599","display_name":"Split-radix FFT algorithm","level":5,"score":0.4000000059604645},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3799000084400177},{"id":"https://openalex.org/C50826107","wikidata":"https://www.wikidata.org/wiki/Q5475803","display_name":"Fourier transform on finite groups","level":5,"score":0.36239999532699585},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3582000136375427},{"id":"https://openalex.org/C122444316","wikidata":"https://www.wikidata.org/wiki/Q1440048","display_name":"Discrete-time Fourier transform","level":5,"score":0.34279999136924744},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.33219999074935913},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C67757890","wikidata":"https://www.wikidata.org/wiki/Q1567607","display_name":"Hartley transform","level":5,"score":0.29789999127388},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.2962000072002411},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C167058841","wikidata":"https://www.wikidata.org/wiki/Q971039","display_name":"Discrete sine transform","level":5,"score":0.26829999685287476},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26089999079704285},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/nla.2331","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.2331","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.03011","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.03011","pdf_url":"https://arxiv.org/pdf/2003.03011","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt9jf6s82b","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/9jf6s82b","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numerical Linear Algebra with Applications, vol 28, iss 1","raw_type":"article"},{"id":"pmh:oai:osti.gov:1786518","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1786518","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2003.03011","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.03011","pdf_url":"https://arxiv.org/pdf/2003.03011","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3309287399","display_name":null,"funder_award_id":"DE\u2010AC02\u201005CH11231","funder_id":"https://openalex.org/F4320338292","funder_display_name":"Lawrence Berkeley National Laboratory"}],"funders":[{"id":"https://openalex.org/F4320338292","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1571240009","https://openalex.org/W1722765662","https://openalex.org/W1975720704","https://openalex.org/W1979502974","https://openalex.org/W2020084487","https://openalex.org/W2027137686","https://openalex.org/W2061171222","https://openalex.org/W2118588482","https://openalex.org/W2134572726","https://openalex.org/W2167797265","https://openalex.org/W2171426752","https://openalex.org/W2258054274","https://openalex.org/W2990961515","https://openalex.org/W3023478445","https://openalex.org/W4235490748","https://openalex.org/W6675137282"],"related_works":[],"abstract_inverted_index":{"Summary":[0],"The":[1,31],"fast":[2],"Fourier":[3,45,57,94],"transform":[4,46,58,95],"(FFT)":[5],"is":[6,156,181,186],"one":[7],"of":[8,14,26,42,69,76,86,96,113,148,164,178,204,207,215],"the":[9,15,43,55,66,70,84,92,121,134,142,145,149,205],"most":[10],"successful":[11],"numerical":[12],"algorithms":[13],"20th":[16],"century":[17],"and":[18,29,152],"has":[19],"found":[20],"numerous":[21],"applications":[22],"in":[23,188],"many":[24],"branches":[25],"computational":[27],"science":[28],"engineering.":[30],"FFT":[32,71,135],"algorithm":[33,123,136],"can":[34,60,110],"be":[35,61],"derived":[36,62],"from":[37,210],"a":[38,100,108,130,138,153,161,165,170,211],"particular":[39],"matrix":[40,72,146,151,212],"decomposition":[41,73,147,168],"discrete":[44,93],"(DFT)":[47],"matrix.":[48],"In":[49],"this":[50,87,189,194],"paper,":[51],"we":[52,192],"show":[53],"that":[54,119],"quantum":[56,116,131,154,179,208],"(QFT)":[59],"by":[63],"further":[64],"decomposing":[65],"diagonal":[67],"factors":[68],"into":[74],"products":[75],"matrices":[77],"with":[78],"Kronecker":[79,88],"product":[80,89],"structure.":[81],"We":[82,103,158],"analyze":[83],"implication":[85],"structure":[90,109],"on":[91,99,129,137],"rank\u20101":[97],"tensors":[98],"classical":[101,139],"computer.":[102,140],"also":[104,159],"explain":[105],"why":[106],"such":[107],"take":[111],"advantage":[112],"an":[114,126],"important":[115],"computer":[117,132],"feature":[118],"enables":[120],"QFT":[122,167,173],"to":[124,169,183,199],"attain":[125],"exponential":[127],"speedup":[128],"over":[133],"Further,":[141],"connection":[143],"between":[144],"DFT":[150],"circuit":[155],"made.":[157],"discuss":[160],"natural":[162],"extension":[163],"radix\u20102":[166],"radix\u2010":[171],"d":[172],"decomposition.":[174],"No":[175],"prior":[176],"knowledge":[177],"computing":[180,209],"required":[182],"understand":[184],"what":[185],"presented":[187],"paper.":[190],"Yet,":[191],"believe":[193],"paper":[195],"may":[196],"help":[197],"readers":[198],"gain":[200],"some":[201],"rudimentary":[202],"understanding":[203],"nature":[206],"computation":[213],"point":[214],"view.":[216]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-03-13T00:00:00"}