{"id":"https://openalex.org/W2112989388","doi":"https://doi.org/10.1145/1507244.1507249","title":"An algebra of quantum processes","display_name":"An algebra of quantum processes","publication_year":2009,"publication_date":"2009-04-01","ids":{"openalex":"https://openalex.org/W2112989388","doi":"https://doi.org/10.1145/1507244.1507249","mag":"2112989388"},"language":"en","primary_location":{"id":"doi:10.1145/1507244.1507249","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1507244.1507249","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"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 Computational Logic","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/A5023088481","display_name":"Mingsheng Ying","orcid":"https://orcid.org/0000-0003-4847-702X"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["AU","CN"],"is_corresponding":false,"raw_author_name":"Mingsheng Ying","raw_affiliation_strings":["Tsinghua University, Beijing, China and University of Technology, Sydney, Ultimo, Australia","Tsinghua University, Beijing, China and University of Technology, Sydney, Ultimo, Australia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University, Beijing, China and University of Technology, Sydney, Ultimo, Australia","institution_ids":["https://openalex.org/I114017466","https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua University, Beijing, China and University of Technology, Sydney, Ultimo, Australia#TAB#","institution_ids":["https://openalex.org/I114017466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022869475","display_name":"Yuan Feng","orcid":"https://orcid.org/0000-0002-3097-3896"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Feng","raw_affiliation_strings":["Tsinghua University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109830244","display_name":"Runyao Duan","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Runyao Duan","raw_affiliation_strings":["Tsinghua University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043930796","display_name":"Zhengfeng Ji","orcid":"https://orcid.org/0000-0002-7659-3178"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengfeng Ji","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.0825,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.96001289,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"10","issue":"3","first_page":"1","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9991000294685364,"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":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bisimulation","display_name":"Bisimulation","score":0.9339163303375244},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6064565777778625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5684036612510681},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5347883105278015},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5268394351005554},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5099755525588989},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5034562945365906},{"id":"https://openalex.org/keywords/process-calculus","display_name":"Process calculus","score":0.4705764651298523},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.455900639295578},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4489799439907074},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3343714475631714},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3306712508201599},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31449347734451294},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2968895137310028},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26480984687805176},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12999099493026733},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06625175476074219}],"concepts":[{"id":"https://openalex.org/C135315306","wikidata":"https://www.wikidata.org/wiki/Q866364","display_name":"Bisimulation","level":2,"score":0.9339163303375244},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6064565777778625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5684036612510681},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5347883105278015},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5268394351005554},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5099755525588989},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5034562945365906},{"id":"https://openalex.org/C161771561","wikidata":"https://www.wikidata.org/wiki/Q1970286","display_name":"Process calculus","level":2,"score":0.4705764651298523},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.455900639295578},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4489799439907074},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3343714475631714},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3306712508201599},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31449347734451294},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2968895137310028},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26480984687805176},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12999099493026733},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06625175476074219},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1507244.1507249","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1507244.1507249","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"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 Computational Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.219.4721","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.4721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.acm.org/tocl/accepted/359ying.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.249.4547","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.4547","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0707.0330v1.pdf","raw_type":"text"},{"id":"pmh:oai:opus.lib.uts.edu.au:10453/9122","is_oa":false,"landing_page_url":"http://hdl.handle.net/10453/9122","pdf_url":null,"source":{"id":"https://openalex.org/S4306401357","display_name":"UTS ePRESS (University of Technology Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114017466","host_organization_name":"University of Technology Sydney","host_organization_lineage":["https://openalex.org/I114017466"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4598437182","display_name":null,"funder_award_id":"2007CB807901","funder_id":"https://openalex.org/F4320321540","funder_display_name":"Ministry of Science and Technology of the People's Republic of China"},{"id":"https://openalex.org/G7080421446","display_name":null,"funder_award_id":"6.07E+15","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321540","display_name":"Ministry of Science and Technology of the People's Republic of China","ror":"https://ror.org/027s68j25"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W88975855","https://openalex.org/W1503973138","https://openalex.org/W1527730705","https://openalex.org/W1551877760","https://openalex.org/W1594984608","https://openalex.org/W1597330895","https://openalex.org/W1631356911","https://openalex.org/W1877217628","https://openalex.org/W1980535239","https://openalex.org/W1999626800","https://openalex.org/W1999702075","https://openalex.org/W2003803711","https://openalex.org/W2013672985","https://openalex.org/W2049471987","https://openalex.org/W2064622659","https://openalex.org/W2076218011","https://openalex.org/W2107914128","https://openalex.org/W2138203529","https://openalex.org/W2152081604","https://openalex.org/W2159566537","https://openalex.org/W2163036762","https://openalex.org/W2912462169","https://openalex.org/W3102057473","https://openalex.org/W3128301419","https://openalex.org/W4285719527","https://openalex.org/W6630104300"],"related_works":["https://openalex.org/W1547524815","https://openalex.org/W2951374406","https://openalex.org/W4300624557","https://openalex.org/W2091970733","https://openalex.org/W3020829080","https://openalex.org/W1532145728","https://openalex.org/W3081656401","https://openalex.org/W2560421581","https://openalex.org/W4247534063","https://openalex.org/W2166928437"],"abstract_inverted_index":{"We":[0],"introduce":[1,91],"an":[2],"algebra":[3],"qCCS":[4,36,52],"of":[5,35,41,64,67,94,104,114,143,156,164],"pure":[6],"quantum":[7,14,109,144,157],"processes":[8,49,80,158],"in":[9,39,51,74,108,161],"which":[10,97],"communications":[11],"by":[12,23,140],"moving":[13],"states":[15],"physically":[16],"are":[17,21,60,126,138],"allowed":[18],"and":[19,55,87,106,122,135],"computations":[20],"modeled":[22,50],"super-operators,":[24],"but":[25],"no":[26],"classical":[27],"data":[28],"is":[29,37,53,81,98,129],"explicitly":[30],"involved.":[31],"An":[32],"operational":[33],"semantics":[34],"presented":[38],"terms":[40],"(nonprobabilistic)":[42],"labeled":[43],"transition":[44],"systems.":[45,110],"Strong":[46],"bisimulation":[47,89,117,120],"between":[48,79],"defined,":[54],"its":[56,123,165],"fundamental":[57],"algebraic":[58],"properties":[59],"established,":[61],"including":[62],"uniqueness":[63],"the":[65,92,162],"solutions":[66],"recursive":[68],"equations.":[69],"To":[70],"model":[71],"sequential":[72],"computation":[73,105],"qCCS,":[75],"a":[76,99,112,150],"reduction":[77,85,124],"relation":[78,86],"defined.":[82],"By":[83],"combining":[84],"strong":[88,95,115,119],"we":[90],"notion":[93,113],"reduction-bisimulation,":[96],"device":[100],"for":[101,153],"observing":[102,154],"interaction":[103],"communication":[107],"Finally,":[111],"approximate":[116,133,136],"(equivalently,":[118],"distance)":[121],"counterpart":[125],"introduced.":[127],"It":[128],"proved":[130],"that":[131],"both":[132],"bisimilarity":[134],"reduction-bisimilarity":[137],"preserved":[139],"various":[141],"constructors":[142],"processes.":[145],"This":[146],"provides":[147],"us":[148],"with":[149],"formal":[151],"tool":[152],"robustness":[155],"against":[159],"inaccuracy":[160],"implementation":[163],"elementary":[166],"gates.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":10}],"updated_date":"2026-06-12T08:23:45.883708","created_date":"2025-10-10T00:00:00"}