{"id":"https://openalex.org/W3093863919","doi":"https://doi.org/10.1109/mcse.2020.3023979","title":"A Comparison of Quantum and Traditional Fourier Transform Computations","display_name":"A Comparison of Quantum and Traditional Fourier Transform Computations","publication_year":2020,"publication_date":"2020-09-15","ids":{"openalex":"https://openalex.org/W3093863919","doi":"https://doi.org/10.1109/mcse.2020.3023979","mag":"3093863919"},"language":"en","primary_location":{"id":"doi:10.1109/mcse.2020.3023979","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mcse.2020.3023979","pdf_url":null,"source":{"id":"https://openalex.org/S107923245","display_name":"Computing in Science & Engineering","issn_l":"1521-9615","issn":["1521-9615","1558-366X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320061","host_organization_name":"AIP Publishing","host_organization_lineage":["https://openalex.org/P4310320061","https://openalex.org/P4310320257"],"host_organization_lineage_names":["AIP Publishing","American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing in Science &amp; Engineering","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/A5090075227","display_name":"Damian Musk","orcid":"https://orcid.org/0000-0001-7643-5615"},"institutions":[{"id":"https://openalex.org/I139025015","display_name":"Pioneer (United States)","ror":"https://ror.org/05jke7315","country_code":"US","type":"company","lineage":["https://openalex.org/I139025015","https://openalex.org/I4210104019"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. R. Musk","raw_affiliation_strings":["Pioneer Academics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pioneer Academics","institution_ids":["https://openalex.org/I139025015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090075227"],"corresponding_institution_ids":["https://openalex.org/I139025015"],"apc_list":null,"apc_paid":null,"fwci":1.043,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.8248015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"22","issue":"6","first_page":"103","last_page":"110"},"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9969000220298767,"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":0.9724000096321106,"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/fourier-transform","display_name":"Fourier transform","score":0.6713885068893433},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.653992772102356},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.6294701099395752},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6170967221260071},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.5816152095794678},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5335192084312439},{"id":"https://openalex.org/keywords/quantum-fourier-transform","display_name":"Quantum Fourier transform","score":0.5204434990882874},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5193554162979126},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5012946128845215},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4998602867126465},{"id":"https://openalex.org/keywords/quantum-complexity-theory","display_name":"Quantum complexity theory","score":0.4979074001312256},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4526890516281128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4287584125995636},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.414113312959671},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3875504434108734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38042914867401123},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37907689809799194},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2182338535785675},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18820664286613464},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13637477159500122},{"id":"https://openalex.org/keywords/quantum-simulator","display_name":"Quantum simulator","score":0.11850866675376892}],"concepts":[{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6713885068893433},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.653992772102356},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.6294701099395752},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6170967221260071},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.5816152095794678},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5335192084312439},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.5204434990882874},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5193554162979126},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5012946128845215},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4998602867126465},{"id":"https://openalex.org/C92043244","wikidata":"https://www.wikidata.org/wiki/Q7269023","display_name":"Quantum complexity theory","level":4,"score":0.4979074001312256},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4526890516281128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4287584125995636},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.414113312959671},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3875504434108734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38042914867401123},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37907689809799194},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2182338535785675},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18820664286613464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13637477159500122},{"id":"https://openalex.org/C161166931","wikidata":"https://www.wikidata.org/wiki/Q7269096","display_name":"Quantum simulator","level":4,"score":0.11850866675376892},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/mcse.2020.3023979","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mcse.2020.3023979","pdf_url":null,"source":{"id":"https://openalex.org/S107923245","display_name":"Computing in Science & Engineering","issn_l":"1521-9615","issn":["1521-9615","1558-366X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320061","host_organization_name":"AIP Publishing","host_organization_lineage":["https://openalex.org/P4310320061","https://openalex.org/P4310320257"],"host_organization_lineage_names":["AIP Publishing","American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing in Science &amp; Engineering","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/W47372315","https://openalex.org/W1965765304","https://openalex.org/W1978477025","https://openalex.org/W2089352162","https://openalex.org/W2101903351","https://openalex.org/W2104590612","https://openalex.org/W2122219982","https://openalex.org/W2168676717","https://openalex.org/W2221627756","https://openalex.org/W2559782415","https://openalex.org/W4243017971","https://openalex.org/W6601903322","https://openalex.org/W6684830772","https://openalex.org/W6730265819"],"related_works":["https://openalex.org/W3136237069","https://openalex.org/W2801113937","https://openalex.org/W2065276051","https://openalex.org/W2952898040","https://openalex.org/W2891491794","https://openalex.org/W2138874081","https://openalex.org/W1978883801","https://openalex.org/W4237826702","https://openalex.org/W4238949871","https://openalex.org/W2962751663"],"abstract_inverted_index":{"The":[0],"quantum":[1,85],"Fourier":[2,8],"transform":[3,9],"(QFT)":[4],"can":[5],"calculate":[6],"the":[7,25,39,44,59,76,81,88,95,99,125,128,131],"of":[10,13,28,71,97,115,127,130],"a":[11,68,112],"vector":[12],"size":[14],"$N$N":[15],"with":[16],"time":[17],"complexity":[18,27,46,90,96,126],"$\\mathcal":[19,29,48],"{O}(\\log":[20],"^2~N)$O(log2N)":[21],"as":[22,79,122,124],"compared":[23],"to":[24,37],"classical":[26],"{O}(N":[30,49],"\\;\\log":[31,50],"N)$O(NlogN).":[32],"However,":[33],"if":[34,92],"one":[35,93],"wanted":[36],"measure":[38],"full":[40],"output":[41,77],"state,":[42],"then":[43],"QFT":[45,132],"becomes":[47],"^2~N)$O(Nlog2N),":[51],"thus":[52],"losing":[53],"its":[54],"apparent":[55],"advantage,":[56],"indicating":[57],"that":[58],"advantage":[60],"is":[61,73,80,107],"fully":[62],"exploited":[63],"for":[64],"algorithms":[65,117],"when":[66],"only":[67],"limited":[69],"number":[70],"samples":[72],"required":[74],"from":[75],"vector,":[78],"case":[82],"in":[83,133],"many":[84],"algorithms.":[86],"Moreover,":[87],"computational":[89],"worsens":[91],"considers":[94],"constructing":[98],"initial":[100],"state.":[101],"In":[102],"this":[103,105],"article,":[104],"issue":[106],"better":[108],"illustrated":[109],"by":[110],"providing":[111],"concrete":[113],"implementation":[114],"these":[116],"and":[118],"discussing":[119],"their":[120],"complexities":[121],"well":[123],"simulation":[129],"matlab.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
