{"id":"https://openalex.org/W2203382396","doi":"https://doi.org/10.1109/tcad.2015.2459034","title":"QMDDs: Efficient Quantum Function Representation and Manipulation","display_name":"QMDDs: Efficient Quantum Function Representation and Manipulation","publication_year":2015,"publication_date":"2015-07-21","ids":{"openalex":"https://openalex.org/W2203382396","doi":"https://doi.org/10.1109/tcad.2015.2459034","mag":"2203382396"},"language":"en","primary_location":{"id":"doi:10.1109/tcad.2015.2459034","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2015.2459034","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","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/A5102787662","display_name":"Philipp Niemann","orcid":"https://orcid.org/0000-0003-0826-0985"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Philipp Niemann","raw_affiliation_strings":["University of Bremen, Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bremen, Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004214923","display_name":"Robert Wille","orcid":"https://orcid.org/0000-0002-4993-7860"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Robert Wille","raw_affiliation_strings":["DFKI GmbH, Bremen, Germany","University of Bremen, Bremen, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4993-7860","affiliations":[{"raw_affiliation_string":"DFKI GmbH, Bremen, Germany","institution_ids":[]},{"raw_affiliation_string":"University of Bremen, Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102000362","display_name":"D. Michael Miller","orcid":"https://orcid.org/0000-0002-4140-3370"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"David Michael Miller","raw_affiliation_strings":["University of Victoria, Victoria, BC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Victoria, Victoria, BC, Canada","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082009815","display_name":"Mitchell A. Thornton","orcid":"https://orcid.org/0000-0003-3559-9511"},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mitchell A. Thornton","raw_affiliation_strings":["Lyle School of Engineering, Southern Methodist University, Dallas, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lyle School of Engineering, Southern Methodist University, Dallas, TX, USA","institution_ids":["https://openalex.org/I178169726"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071742136","display_name":"Rolf Drechsler","orcid":"https://orcid.org/0000-0002-9872-1740"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rolf Drechsler","raw_affiliation_strings":["DFKI GmbH, Bremen, Germany","University of Bremen, Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DFKI GmbH, Bremen, Germany","institution_ids":[]},{"raw_affiliation_string":"University of Bremen, Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.1672,"has_fulltext":false,"cited_by_count":131,"citation_normalized_percentile":{"value":0.97812066,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"35","issue":"1","first_page":"86","last_page":"99"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","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/T10020","display_name":"Quantum Information and Cryptography","score":0.9948999881744385,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.989300012588501,"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/quantum-computer","display_name":"Quantum computer","score":0.6331163644790649},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6250740885734558},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.5854305624961853},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5807384848594666},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5575921535491943},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5427780747413635},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.5272176265716553},{"id":"https://openalex.org/keywords/quantum-process","display_name":"Quantum process","score":0.5226073861122131},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5051098465919495},{"id":"https://openalex.org/keywords/influence-diagram","display_name":"Influence diagram","score":0.4331912398338318},{"id":"https://openalex.org/keywords/quantum-dynamics","display_name":"Quantum dynamics","score":0.18177497386932373},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16741329431533813},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16208305954933167},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15206974744796753}],"concepts":[{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.6331163644790649},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6250740885734558},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.5854305624961853},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5807384848594666},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5575921535491943},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5427780747413635},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.5272176265716553},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.5226073861122131},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5051098465919495},{"id":"https://openalex.org/C20837028","wikidata":"https://www.wikidata.org/wiki/Q623966","display_name":"Influence diagram","level":3,"score":0.4331912398338318},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.18177497386932373},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16741329431533813},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16208305954933167},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15206974744796753},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcad.2015.2459034","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2015.2459034","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7300000190734863,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W151360480","https://openalex.org/W162687315","https://openalex.org/W566766357","https://openalex.org/W1231265883","https://openalex.org/W1631356911","https://openalex.org/W2003043756","https://openalex.org/W2038749191","https://openalex.org/W2069313594","https://openalex.org/W2080267935","https://openalex.org/W2084652510","https://openalex.org/W2106850456","https://openalex.org/W2121695129","https://openalex.org/W2132833274","https://openalex.org/W2135674876","https://openalex.org/W2145557978","https://openalex.org/W2149479807","https://openalex.org/W2150505294","https://openalex.org/W2153132662","https://openalex.org/W2159226773","https://openalex.org/W2168676717","https://openalex.org/W2764347725","https://openalex.org/W2949516668","https://openalex.org/W3216272643","https://openalex.org/W4235800851","https://openalex.org/W4250447890","https://openalex.org/W4285719527","https://openalex.org/W4378744510","https://openalex.org/W6606648485","https://openalex.org/W6628278774","https://openalex.org/W6680164786","https://openalex.org/W6681975683"],"related_works":["https://openalex.org/W2409877639","https://openalex.org/W4388704119","https://openalex.org/W2910123824","https://openalex.org/W4213379151","https://openalex.org/W3206120658","https://openalex.org/W2911278742","https://openalex.org/W1889203613","https://openalex.org/W4281550036","https://openalex.org/W2045780663","https://openalex.org/W1495512171"],"abstract_inverted_index":{"Quantum":[0,42,128],"mechanical":[1,34,68],"phenomena":[2,69],"such":[3],"as":[4],"phase":[5],"shifts,":[6],"superposition,":[7],"and":[8,21,26,94,141,166,238,240,255],"entanglement":[9],"show":[10,241],"promise":[11],"in":[12,37,59,113,162,180,205],"use":[13,237],"for":[14,18,91,107,186,202,223,235,249],"computation.":[15],"Suitable":[16],"technologies":[17],"the":[19,38,48,60,74,80,108,155,171,174,194,224,243,261],"modeling":[20],"design":[22],"of":[23,40,50,66,82,96,110,115,158,173,192,197,221,263],"quantum":[24,33,67,84,97,111,152,203,226],"computers":[25],"other":[27],"information":[28],"processing":[29],"techniques":[30],"that":[31,44,242],"exploit":[32],"principles":[35],"are":[36,70,134],"range":[39],"vision.":[41],"algorithms":[43],"significantly":[45,231],"speed":[46],"up":[47],"process":[49],"solving":[51],"several":[52],"important":[53,247],"computation":[54],"problems":[55],"have":[56,118],"been":[57,119,209],"proposed":[58],"past.":[61],"The":[62],"most":[63],"common":[64],"representation":[65,93,109,245],"transformation":[71,75,139],"matrices.":[72],"However,":[73,154],"matrices":[76,140],"grow":[77],"exponentially":[78],"with":[79],"size":[81],"a":[83,163,218,250],"system":[85],"and,":[86],"thus,":[87],"pose":[88],"significant":[89],"challenges":[90],"efficient":[92],"manipulation":[95,239],"functionality.":[98],"In":[99,213],"order":[100],"to":[101,136],"address":[102],"this":[103,214],"problem,":[104],"first":[105],"approaches":[106],"systems":[112],"terms":[114],"decision":[116,181,200,251],"diagrams":[117,182,201],"proposed.":[120],"One":[121],"very":[122],"promising":[123],"approach":[124],"is":[125,184],"given":[126],"by":[127,149],"Multiple-Valued":[129],"Decision":[130],"Diagrams":[131],"(QMDDs)":[132],"which":[133,183],"able":[135],"efficiently":[137],"represent":[138],"also":[142],"inherently":[143],"support":[144],"multiple-valued":[145],"basis":[146,165],"states":[147],"offered":[148],"many":[150],"physical":[151],"systems.":[153],"initial":[156],"proposal":[157],"QMDDs":[159,198,222],"was":[160],"lacking":[161],"formal":[164],"did":[167],"not":[168,208],"allow,":[169],"e.g.,":[170],"change":[172],"variable":[175],"order-an":[176],"established":[177],"core":[178],"functionality":[179,204],"crucial":[185],"determining":[187],"more":[188],"compact":[189],"representations.":[190],"Because":[191],"this,":[193],"full":[195],"potential":[196],"or":[199],"general":[206,225],"has":[207],"fully":[210],"exploited":[211],"yet.":[212],"paper,":[215],"we":[216,229],"present":[217],"refined":[219],"definition":[220],"case.":[227],"Furthermore,":[228],"provide":[230],"improved":[232],"computational":[233],"methods":[234],"their":[236],"resulting":[244],"satisfies":[246],"criteria":[248],"diagram,":[252],"i.e.,":[253],"compactness":[254],"canonicity.":[256],"An":[257],"experimental":[258],"evaluation":[259],"confirms":[260],"efficiency":[262],"QMDDs.":[264]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":20},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
