{"id":"https://openalex.org/W4406548097","doi":"https://doi.org/10.1007/s00224-024-10208-5","title":"Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection","display_name":"Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection","publication_year":2025,"publication_date":"2025-01-17","ids":{"openalex":"https://openalex.org/W4406548097","doi":"https://doi.org/10.1007/s00224-024-10208-5"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-024-10208-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-024-10208-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-024-10208-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00224-024-10208-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000386979","display_name":"Ryo Hiromasa","orcid":"https://orcid.org/0000-0003-1273-766X"},"institutions":[{"id":"https://openalex.org/I4210133125","display_name":"Mitsubishi Electric (Japan)","ror":"https://ror.org/033y26782","country_code":"JP","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Ryo Hiromasa","raw_affiliation_strings":["Information Technology R&D Center, Mitsubishi Electric Corporation, 5-1-1 Ofuna, Kamakura, Kanagawa, 247-8501, Japan"],"affiliations":[{"raw_affiliation_string":"Information Technology R&D Center, Mitsubishi Electric Corporation, 5-1-1 Ofuna, Kamakura, Kanagawa, 247-8501, Japan","institution_ids":["https://openalex.org/I4210133125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103259252","display_name":"Akihiro Mizutani","orcid":"https://orcid.org/0009-0008-5161-253X"},"institutions":[{"id":"https://openalex.org/I42766147","display_name":"University of Toyama","ror":"https://ror.org/0445phv87","country_code":"JP","type":"education","lineage":["https://openalex.org/I42766147"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akihiro Mizutani","raw_affiliation_strings":["Faculty of Engineering, University of Toyama, Gofuku 3190, Toyama, 930-8555, Japan"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, University of Toyama, Gofuku 3190, Toyama, 930-8555, Japan","institution_ids":["https://openalex.org/I42766147"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085793321","display_name":"Yuki Takeuchi","orcid":"https://orcid.org/0000-0003-2428-7432"},"institutions":[{"id":"https://openalex.org/I4210105847","display_name":"NTT Basic Research Laboratories","ror":"https://ror.org/01m2pas06","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210105847"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuki Takeuchi","raw_affiliation_strings":["NTT Communication Science Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, 243-0198, Japan","NTT Research Center for Theoretical Quantum Information, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, 243-0198, Japan"],"affiliations":[{"raw_affiliation_string":"NTT Communication Science Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, 243-0198, Japan","institution_ids":[]},{"raw_affiliation_string":"NTT Research Center for Theoretical Quantum Information, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, 243-0198, Japan","institution_ids":["https://openalex.org/I4210105847"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062521166","display_name":"Seiichiro Tani","orcid":"https://orcid.org/0000-0002-6041-1704"},"institutions":[{"id":"https://openalex.org/I4210105847","display_name":"NTT Basic Research Laboratories","ror":"https://ror.org/01m2pas06","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210105847"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Seiichiro Tani","raw_affiliation_strings":["NTT Communication Science Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, 243-0198, Japan","NTT Research Center for Theoretical Quantum Information, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, 243-0198, Japan"],"affiliations":[{"raw_affiliation_string":"NTT Communication Science Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, 243-0198, Japan","institution_ids":[]},{"raw_affiliation_string":"NTT Research Center for Theoretical Quantum Information, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, 243-0198, Japan","institution_ids":["https://openalex.org/I4210105847"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5000386979"],"corresponding_institution_ids":["https://openalex.org/I4210133125"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":2.6916,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.88671836,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"69","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":0.9998999834060669,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9998000264167786,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9997000098228455,"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-cloning","display_name":"Quantum cloning","score":0.61192786693573},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6039970517158508},{"id":"https://openalex.org/keywords/cloning","display_name":"Cloning (programming)","score":0.5561078786849976},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5198538899421692},{"id":"https://openalex.org/keywords/postselection","display_name":"Postselection","score":0.4971978962421417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40671101212501526},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.40386760234832764},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.3922886252403259},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.39225339889526367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3716908097267151},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27403271198272705},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2669975459575653},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2617184519767761},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.25579071044921875},{"id":"https://openalex.org/keywords/quantum-network","display_name":"Quantum network","score":0.14351552724838257},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08708798885345459},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.05459940433502197}],"concepts":[{"id":"https://openalex.org/C2776887110","wikidata":"https://www.wikidata.org/wiki/Q7269018","display_name":"Quantum cloning","level":5,"score":0.61192786693573},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6039970517158508},{"id":"https://openalex.org/C121050878","wikidata":"https://www.wikidata.org/wiki/Q5135020","display_name":"Cloning (programming)","level":2,"score":0.5561078786849976},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5198538899421692},{"id":"https://openalex.org/C2777061846","wikidata":"https://www.wikidata.org/wiki/Q7234498","display_name":"Postselection","level":4,"score":0.4971978962421417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40671101212501526},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.40386760234832764},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3922886252403259},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39225339889526367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3716908097267151},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27403271198272705},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2669975459575653},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2617184519767761},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25579071044921875},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.14351552724838257},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08708798885345459},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.05459940433502197}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00224-024-10208-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-024-10208-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-024-10208-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00224-024-10208-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-024-10208-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-024-10208-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406548097.pdf","grobid_xml":"https://content.openalex.org/works/W4406548097.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W20286062","https://openalex.org/W1546864018","https://openalex.org/W1575325906","https://openalex.org/W1590419653","https://openalex.org/W1861265746","https://openalex.org/W1910288008","https://openalex.org/W1965861766","https://openalex.org/W1969406948","https://openalex.org/W1993292204","https://openalex.org/W1993797543","https://openalex.org/W1999502904","https://openalex.org/W2007000413","https://openalex.org/W2033216491","https://openalex.org/W2035878963","https://openalex.org/W2035993353","https://openalex.org/W2040958198","https://openalex.org/W2049471987","https://openalex.org/W2061949491","https://openalex.org/W2069170136","https://openalex.org/W2069280326","https://openalex.org/W2085142809","https://openalex.org/W2098767285","https://openalex.org/W2117593045","https://openalex.org/W2134677596","https://openalex.org/W2158764863","https://openalex.org/W2465235335","https://openalex.org/W2482126025","https://openalex.org/W2517871044","https://openalex.org/W2548241038","https://openalex.org/W2560356194","https://openalex.org/W2601939557","https://openalex.org/W2604110432","https://openalex.org/W2610451291","https://openalex.org/W2754797405","https://openalex.org/W2756364467","https://openalex.org/W2772471500","https://openalex.org/W2897579646","https://openalex.org/W2963245216","https://openalex.org/W2990616282","https://openalex.org/W3023478445","https://openalex.org/W3037725046","https://openalex.org/W3098301704","https://openalex.org/W3100111077","https://openalex.org/W3102634331","https://openalex.org/W4298227433","https://openalex.org/W6613827064"],"related_works":["https://openalex.org/W1993461124","https://openalex.org/W2310510976","https://openalex.org/W2003694878","https://openalex.org/W1987749534","https://openalex.org/W2112723541","https://openalex.org/W1985540967","https://openalex.org/W2007937610","https://openalex.org/W4301381449","https://openalex.org/W2951568242","https://openalex.org/W2033967965"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"define":[2,11],"rewinding":[3,47,150],"operators":[4],"that":[5,59,89,106,119,147,157,166],"invert":[6],"quantum":[7,40,142,161,176],"measurements.":[8],"Then,":[9],"we":[10,87,144,164],"complexity":[12],"classes":[13],"$$\\textsf{RwBQP}$$":[14],"<mml:math":[15,21,28,63,94,122,186],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[16,22,29,64,95,123,187],"<mml:mi>RwBQP</mml:mi>":[17,71],"</mml:math>":[18,24,31,79,97,129,189],",":[19,25,130],"$$\\textsf{CBQP}$$":[20],"<mml:mi>CBQP</mml:mi>":[23,73],"and":[26,51],"$$\\textsf{AdPostBQP}$$":[27],"<mml:mi>AdPostBQP</mml:mi>":[30,75],"as":[32],"sets":[33],"of":[34,46,84,104],"decision":[35],"problems":[36],"solvable":[37],"by":[38],"polynomial-size":[39],"circuits":[41,169,179],"with":[42,101,108,141],"a":[43,82,148],"polynomial":[44,177],"number":[45],"operators,":[48,50],"cloning":[49],"adaptive":[52],"postselections,":[53],"respectively.":[54],"Our":[55],"main":[56],"result":[57],"is":[58,152],"$$\\textsf{BPP}^\\textsf{PP}\\subseteq":[60],"\\textsf{RwBQP}=\\textsf{CBQP}=\\textsf{AdPostBQP}\\subseteq":[61],"\\textsf{PSPACE}$$":[62],"<mml:mrow>":[65,124],"<mml:msup>":[66],"<mml:mi>BPP</mml:mi>":[67],"<mml:mi>PP</mml:mi>":[68,188],"</mml:msup>":[69],"<mml:mo>\u2286</mml:mo>":[70,76],"<mml:mo>=</mml:mo>":[72,74],"<mml:mi>PSPACE</mml:mi>":[77],"</mml:mrow>":[78,128],".":[80,190],"As":[81],"byproduct":[83],"this":[85],"result,":[86],"show":[88,146,165],"any":[90,182],"problem":[91,136,183],"in":[92,184],"$$\\textsf{PostBQP}$$":[93],"<mml:mi>PostBQP</mml:mi>":[96],"can":[98,180],"be":[99,138],"solved":[100,140],"only":[102],"postselections":[103],"events":[105],"occur":[107],"probabilities":[109],"polynomially":[110],"close":[111],"to":[112,154],"one.":[113],"Under":[114],"the":[115,132],"strongly":[116],"believed":[117],"assumption":[118],"$$\\textsf{BQP}\\nsupseteq":[120],"\\textsf{SZK}$$":[121],"<mml:mi>BQP</mml:mi>":[125],"<mml:mo>\u2289</mml:mo>":[126],"<mml:mi>SZK</mml:mi>":[127],"or":[131],"shortest":[133],"independent":[134],"vectors":[135],"cannot":[137],"efficiently":[139],"computers,":[143],"also":[145],"single":[149],"operator":[151],"sufficient":[153],"achieve":[155],"tasks":[156],"are":[158],"intractable":[159],"for":[160],"computation.":[162],"Finally,":[163],"rewindable":[167,174],"Clifford":[168],"remain":[170],"classically":[171],"simulatable,":[172],"but":[173],"instantaneous":[175],"time":[178],"solve":[181],"$$\\textsf{PP}$$":[185]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}