{"id":"https://openalex.org/W2772471500","doi":"https://doi.org/10.22331/q-2018-11-15-106","title":"Merlin-Arthur with efficient quantum Merlin and quantum supremacy for the second level of the Fourier hierarchy","display_name":"Merlin-Arthur with efficient quantum Merlin and quantum supremacy for the second level of the Fourier hierarchy","publication_year":2018,"publication_date":"2018-11-15","ids":{"openalex":"https://openalex.org/W2772471500","doi":"https://doi.org/10.22331/q-2018-11-15-106","mag":"2772471500"},"language":"en","primary_location":{"id":"doi:10.22331/q-2018-11-15-106","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2018-11-15-106","pdf_url":"https://quantum-journal.org/papers/q-2018-11-15-106/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2018-11-15-106/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Tomoyuki Morimae","orcid":null},"institutions":[{"id":"https://openalex.org/I165735259","display_name":"Gunma University","ror":"https://ror.org/046fm7598","country_code":"JP","type":"education","lineage":["https://openalex.org/I165735259"]},{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]},{"id":"https://openalex.org/I4210086780","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19","country_code":"JP","type":"government","lineage":["https://openalex.org/I4210086780"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tomoyuki Morimae","raw_affiliation_strings":["Department of Computer Science, Gunma University, 1-5-1 Tenjincho, Kiryu, Gunma, 376-0052, Japan","JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan","Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Gunma University, 1-5-1 Tenjincho, Kiryu, Gunma, 376-0052, Japan","institution_ids":["https://openalex.org/I165735259"]},{"raw_affiliation_string":"JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan","institution_ids":["https://openalex.org/I4210086780"]},{"raw_affiliation_string":"Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yuki Takeuchi","orcid":null},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuki Takeuchi","raw_affiliation_strings":["Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan","NTT Communication Science Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan","institution_ids":["https://openalex.org/I98285908"]},{"raw_affiliation_string":"NTT Communication Science Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Harumichi Nishimura","orcid":null},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Harumichi Nishimura","raw_affiliation_strings":["Graduate School of Informatics, Nagoya University, Furocho, Chikusaku, Nagoya, Aichi, 464-8601, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Informatics, Nagoya University, Furocho, Chikusaku, Nagoya, Aichi, 464-8601, Japan","institution_ids":["https://openalex.org/I60134161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.1827,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.83755961,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2","issue":null,"first_page":"106","last_page":"106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.8371000289916992,"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":0.8371000289916992,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.07100000232458115,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.01510000042617321,"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":0.5414000153541565},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.527400016784668},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5085999965667725},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.49709999561309814},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.46299999952316284},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.44449999928474426},{"id":"https://openalex.org/keywords/quantum-system","display_name":"Quantum system","score":0.3855000138282776},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.37549999356269836},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.3650999963283539},{"id":"https://openalex.org/keywords/quantum-operation","display_name":"Quantum operation","score":0.3614000082015991}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6154000163078308},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.5414000153541565},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.527400016784668},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.49709999561309814},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.46299999952316284},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4514000117778778},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.44449999928474426},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3855000138282776},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.37549999356269836},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.3614000082015991},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36070001125335693},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.3564999997615814},{"id":"https://openalex.org/C165973109","wikidata":"https://www.wikidata.org/wiki/Q894014","display_name":"Quantum probability","level":5,"score":0.3398999869823456},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3361999988555908},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.3328999876976013},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.32179999351501465},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.3082999885082245},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.30219998955726624},{"id":"https://openalex.org/C169460222","wikidata":"https://www.wikidata.org/wiki/Q1206311","display_name":"Quantum logic","level":4,"score":0.2913999855518341},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2863999903202057},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2858999967575073},{"id":"https://openalex.org/C175225751","wikidata":"https://www.wikidata.org/wiki/Q15927242","display_name":"Discrete Fourier series","level":5,"score":0.2822999954223633},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.26570001244544983},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.2653000056743622},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25780001282691956},{"id":"https://openalex.org/C94231801","wikidata":"https://www.wikidata.org/wiki/Q653850","display_name":"Probability amplitude","level":5,"score":0.2574999928474426},{"id":"https://openalex.org/C58948655","wikidata":"https://www.wikidata.org/wiki/Q7604392","display_name":"Statistical distance","level":3,"score":0.2535000145435333}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2018-11-15-106","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2018-11-15-106","pdf_url":"https://quantum-journal.org/papers/q-2018-11-15-106/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1711.10605","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.10605","pdf_url":"https://arxiv.org/pdf/1711.10605","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:doaj.org/article:7455762127b24466b3dcc256d6aeecae","is_oa":true,"landing_page_url":"https://doaj.org/article/7455762127b24466b3dcc256d6aeecae","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 2, p 106 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2018-11-15-106","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2018-11-15-106","pdf_url":"https://quantum-journal.org/papers/q-2018-11-15-106/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2266386893","display_name":null,"funder_award_id":"26247016","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4066534045","display_name":null,"funder_award_id":"JP17J03503","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6894041692","display_name":null,"funder_award_id":"16K00015","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G755662851","display_name":null,"funder_award_id":"16H01705","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8697807446","display_name":null,"funder_award_id":"JP17K12637","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320338111","display_name":"Precursory Research for Embryonic Science and Technology","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2772471500.pdf","grobid_xml":"https://content.openalex.org/works/W2772471500.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W58322429","https://openalex.org/W365259755","https://openalex.org/W1484565144","https://openalex.org/W1494680701","https://openalex.org/W1546864018","https://openalex.org/W1590419653","https://openalex.org/W1770873769","https://openalex.org/W1827590847","https://openalex.org/W1910288008","https://openalex.org/W1977250709","https://openalex.org/W1986130900","https://openalex.org/W1993292204","https://openalex.org/W2033216491","https://openalex.org/W2048118641","https://openalex.org/W2069280326","https://openalex.org/W2102008187","https://openalex.org/W2117584890","https://openalex.org/W2162167669","https://openalex.org/W2168676717","https://openalex.org/W2201916012","https://openalex.org/W2308553311","https://openalex.org/W2573064840","https://openalex.org/W2605573827","https://openalex.org/W2758002822","https://openalex.org/W2897579646","https://openalex.org/W2913788899","https://openalex.org/W3097999405","https://openalex.org/W4243481097","https://openalex.org/W6828377936"],"related_works":[],"abstract_inverted_index":{"We":[0,44,110,166],"introduce":[1],"a":[2,21,60,132,148,201],"simple":[3],"sub-universal":[4,82,102],"quantum":[5,117,159,205],"computing":[6,118],"model,":[7,198],"which":[8,135],"we":[9,130,136],"call":[10,137],"the":[11,37,41,51,64,69,93,113,120,124,138,174,183,187,192,196],"Hadamard-classical":[12],"circuit":[13,24],"with":[14,142,204],"one-qubit":[15],"(HC1Q)":[16],"model.":[17],"It":[18,146],"consists":[19],"of":[20,29,40,50,116,123,157,186],"classical":[22,114,209],"reversible":[23],"sandwiched":[25],"by":[26],"two":[27,158,175],"layers":[28],"Hadamard":[30],"gates,":[31],"and":[32,89,91,208],"therefore":[33,92],"it":[34],"is":[35,75,147,170],"in":[36,119,182],"second":[38,70,121,184],"level":[39,122,185],"Fourier":[42,125,188],"hierarchy.":[43,126],"show":[45,167],"that":[46,104,168],"output":[47,154],"probability":[48,139,155],"distributions":[49,156],"HC1Q":[52,193],"model":[53,194],"cannot":[54],"be":[55,97],"classically":[56,108],"efficiently":[57],"sampled":[58],"within":[59],"multiplicative":[61],"error":[62],"unless":[63],"polynomial-time":[65,206,211],"hierarchy":[66],"collapses":[67],"to":[68,107,151,179],"level.":[71],"The":[72],"proof":[73],"technique":[74,94],"different":[76],"from":[77],"those":[78],"used":[79],"for":[80,99],"previous":[81],"models,":[83],"such":[84,190],"as":[85,191],"IQP,":[86],"Boson":[87],"Sampling,":[88],"DQC1,":[90],"itself":[95],"might":[96],"useful":[98],"finding":[100],"other":[101],"models":[103],"are":[105,161,177],"hard":[106],"simulate.":[109],"also":[111],"study":[112],"verification":[115],"To":[127],"this":[128],"end,":[129],"define":[131],"promise":[133,149],"problem,":[134],"distribution":[140],"distinguishability":[141],"maximum":[143],"norm":[144],"(PDD-Max).":[145],"problem":[150],"decide":[152],"whether":[153],"circuits":[160,176],"far":[162],"apart":[163],"or":[164,195],"close.":[165],"PDD-Max":[169,199],"BQP-complete,":[171],"but":[172],"if":[173],"restricted":[178],"some":[180],"types":[181],"hierarchy,":[189],"IQP":[197],"has":[200],"Merlin-Arthur":[202],"system":[203],"Merlin":[207],"probabilistic":[210],"Arthur.":[212]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2017-12-22T00:00:00"}
