{"id":"https://openalex.org/W3108630003","doi":"https://doi.org/10.22331/q-2020-12-07-369","title":"Synthesis of CNOT-Dihedral circuits with optimal number of two qubit gates","display_name":"Synthesis of CNOT-Dihedral circuits with optimal number of two qubit gates","publication_year":2020,"publication_date":"2020-12-07","ids":{"openalex":"https://openalex.org/W3108630003","doi":"https://doi.org/10.22331/q-2020-12-07-369","mag":"3108630003"},"language":"lv","primary_location":{"id":"doi:10.22331/q-2020-12-07-369","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-12-07-369","pdf_url":"https://quantum-journal.org/papers/q-2020-12-07-369/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-2020-12-07-369/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Shelly Garion","orcid":null},"institutions":[{"id":"https://openalex.org/I4210167297","display_name":"IBM Research - Haifa","ror":"https://ror.org/05rw9t746","country_code":"IL","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210167297"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shelly Garion","raw_affiliation_strings":["IBM Quantum, IBM Research Haifa, Haifa University Campus, Mount Carmel, Haifa, 3498825, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Quantum, IBM Research Haifa, Haifa University Campus, Mount Carmel, Haifa, 3498825, Israel","institution_ids":["https://openalex.org/I4210167297"]}]},{"author_position":"last","author":{"id":null,"display_name":"Andrew W. Cross","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew W. Cross","raw_affiliation_strings":["IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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":0.8125,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79803526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"4","issue":null,"first_page":"369","last_page":"369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.6780999898910522,"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":0.6780999898910522,"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":0.07429999858140945,"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":0.07329999655485153,"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/quantum-gate","display_name":"Quantum gate","score":0.5906000137329102},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5501999855041504},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5335000157356262},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.532800018787384},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.5052000284194946},{"id":"https://openalex.org/keywords/controlled-not-gate","display_name":"Controlled NOT gate","score":0.45320001244544983},{"id":"https://openalex.org/keywords/quantum-circuit","display_name":"Quantum circuit","score":0.4147000014781952},{"id":"https://openalex.org/keywords/logic-gate","display_name":"Logic gate","score":0.4065999984741211},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.35740000009536743}],"concepts":[{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.5906000137329102},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5501999855041504},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5335000157356262},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.532800018787384},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.5052000284194946},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.483599990606308},{"id":"https://openalex.org/C182953411","wikidata":"https://www.wikidata.org/wiki/Q917713","display_name":"Controlled NOT gate","level":5,"score":0.45320001244544983},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43470001220703125},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.4147000014781952},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4097000062465668},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.4065999984741211},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.35740000009536743},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C142465778","wikidata":"https://www.wikidata.org/wiki/Q2502619","display_name":"Toffoli gate","level":5,"score":0.33329999446868896},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3231000006198883},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.29510000348091125},{"id":"https://openalex.org/C190560348","wikidata":"https://www.wikidata.org/wiki/Q3245116","display_name":"Circuit design","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C28495749","wikidata":"https://www.wikidata.org/wiki/Q155516","display_name":"XOR gate","level":3,"score":0.2928999960422516},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C58140894","wikidata":"https://www.wikidata.org/wiki/Q560398","display_name":"OR gate","level":4,"score":0.2888000011444092},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2736999988555908},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2678000032901764},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C10418432","wikidata":"https://www.wikidata.org/wiki/Q560370","display_name":"AND gate","level":3,"score":0.2572999894618988},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2020-12-07-369","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-12-07-369","pdf_url":"https://quantum-journal.org/papers/q-2020-12-07-369/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:2006.12042","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.12042","pdf_url":"https://arxiv.org/pdf/2006.12042","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:b891a57688594996963d8a038d317062","is_oa":true,"landing_page_url":"https://doaj.org/article/b891a57688594996963d8a038d317062","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 4, p 369 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2020-12-07-369","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-12-07-369","pdf_url":"https://quantum-journal.org/papers/q-2020-12-07-369/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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3108630003.pdf","grobid_xml":"https://content.openalex.org/works/W3108630003.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W9166514","https://openalex.org/W1490521149","https://openalex.org/W1532834996","https://openalex.org/W1866699241","https://openalex.org/W1895592099","https://openalex.org/W2017477211","https://openalex.org/W2052146120","https://openalex.org/W2054620262","https://openalex.org/W2062506119","https://openalex.org/W2079099822","https://openalex.org/W2094974378","https://openalex.org/W2102008187","https://openalex.org/W2150528339","https://openalex.org/W2169656062","https://openalex.org/W2170620327","https://openalex.org/W2335841284","https://openalex.org/W2338653245","https://openalex.org/W2410139980","https://openalex.org/W2570901353","https://openalex.org/W2613136543","https://openalex.org/W2617241380","https://openalex.org/W2765570517","https://openalex.org/W2765753692","https://openalex.org/W2771726258","https://openalex.org/W2888334837","https://openalex.org/W2949178668","https://openalex.org/W2963760674","https://openalex.org/W2964026084","https://openalex.org/W3011543520","https://openalex.org/W3012928806","https://openalex.org/W3043678617","https://openalex.org/W3176788313"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"note":[2],"we":[3],"present":[4],"explicit":[5],"canonical":[6],"forms":[7],"for":[8],"all":[9],"the":[10,13,30],"elements":[11],"in":[12],"two-qubit":[14],"CNOT-Dihedral":[15,48],"group,":[16,49],"with":[17],"minimal":[18],"numbers":[19],"of":[20,33,54],"controlled-<mml:math":[21,25,55],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>S</mml:mi></mml:math>(<mml:math":[22],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>C</mml:mi><mml:mi>S</mml:mi></mml:math>)":[23],"and":[24,71],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>X</mml:mi></mml:math>(<mml:math":[26,56],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>C</mml:mi><mml:mi>X</mml:mi></mml:math>)":[27,57],"gates,":[28],"using":[29],"generating":[31],"set":[32],"quantum":[34],"gates<mml:math":[35],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mo":[36],"stretchy=\"false\">[</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi><mml:mi>S</mml:mi><mml:mo":[37],"stretchy=\"false\">]</mml:mo></mml:math>.":[38],"We":[39],"provide":[40],"an":[41,51],"algorithm":[42],"to":[43,63,76],"successively":[44],"construct":[45],"the<mml:math":[46],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>n</mml:mi></mml:math>-qubit":[47],"asserting":[50],"optimal":[52],"number":[53],"gates.":[58],"These":[59],"results":[60],"are":[61],"needed":[62],"estimate":[64],"gate":[65,81],"errors":[66],"via":[67],"non-Clifford":[68],"randomized":[69],"benchmarking":[70],"may":[72],"have":[73],"further":[74],"applications":[75],"circuit":[77],"optimization":[78],"over":[79],"fault-tolerant":[80],"sets.":[82]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2020-12-07T00:00:00"}
