{"id":"https://openalex.org/W2265094020","doi":null,"title":"From Extraspecial Two-Groups To GHZ States","display_name":"From Extraspecial Two-Groups To GHZ States","publication_year":2007,"publication_date":"2007-06-12","ids":{"openalex":"https://openalex.org/W2265094020","mag":"2265094020"},"language":"en","primary_location":{"id":"mag:2265094020","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0706.1761","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0706.1761","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100419793","display_name":"Yong Zhang","orcid":"https://orcid.org/0000-0002-3522-0885","observed_orcids":["https://orcid.org/0000-0002-3522-0885"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yong Zhang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3522-0885","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084951219","display_name":"Eric C. Rowell","orcid":"https://orcid.org/0000-0002-2338-9819","observed_orcids":["https://orcid.org/0000-0002-2338-9819"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eric C. Rowell","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2338-9819","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111491485","display_name":"Yong-Shi Wu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yong-Shi Wu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101752833","display_name":"Zhenghan Wang","orcid":"https://orcid.org/0000-0002-5253-6400","observed_orcids":["https://orcid.org/0000-0002-5253-6400"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhenghan Wang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5253-6400","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.3878999948501587,"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":0.3878999948501587,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.29350000619888306,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.07850000262260437,"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/ghz-states","display_name":"GHZ states","score":0.9670000076293945},{"id":"https://openalex.org/keywords/almost-complex-structures","display_name":"almost complex structures","score":0.968999981880188},{"id":"https://openalex.org/keywords/topological-quantum-computation","display_name":"topological quantum computation","score":0.8740000128746033},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"quantum error correction","score":1.0}],"concepts":[{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.8822650909423828},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.879481852054596},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.7247293591499329},{"id":"https://openalex.org/C147441545","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid theory","level":3,"score":0.6702842116355896},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5787222981452942},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.5670140981674194},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5247424244880676},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.481649786233902},{"id":"https://openalex.org/C32955637","wikidata":"https://www.wikidata.org/wiki/Q684363","display_name":"Special unitary group","level":2,"score":0.47489133477211},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45437946915626526},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3993972837924957},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.38202303647994995},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.36765244603157043},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.34371423721313477},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.29876983165740967},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23865169286727905},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21178513765335083},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.15943863987922668},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.11552003026008606},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.07414689660072327},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2265094020","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0706.1761","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2265094020","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0706.1761","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1569528011","https://openalex.org/W1607440767","https://openalex.org/W1631356911","https://openalex.org/W1977670750","https://openalex.org/W1981095208","https://openalex.org/W1997328257","https://openalex.org/W2000407553","https://openalex.org/W2017156903","https://openalex.org/W2027230080","https://openalex.org/W2037061784","https://openalex.org/W2052372389","https://openalex.org/W2056954154","https://openalex.org/W2059273435","https://openalex.org/W2062292260","https://openalex.org/W2084461821","https://openalex.org/W2084738004","https://openalex.org/W2091331782","https://openalex.org/W2128124629","https://openalex.org/W2135745986","https://openalex.org/W2154434103","https://openalex.org/W2159215733","https://openalex.org/W2167413626","https://openalex.org/W2172159049","https://openalex.org/W2962956712","https://openalex.org/W3102596210","https://openalex.org/W3103359025"],"related_works":["https://openalex.org/W4300819726","https://openalex.org/W2108535227","https://openalex.org/W1977278339","https://openalex.org/W2949786537","https://openalex.org/W6941107644","https://openalex.org/W6903547624","https://openalex.org/W1995169499","https://openalex.org/W2962756189","https://openalex.org/W6948421216","https://openalex.org/W6884755183"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"explore":[4],"natural":[5],"connections":[6],"among":[7],"extraspecial":[8,29,51,115],"2-groups,":[9,116],"almost-complex":[10,34],"structures,":[11],"unitary":[12,42,66,94,105],"representations":[13,27,44,48,68,92],"of":[14,28,33,47,49,79,87,96],"the":[15,19,50,54,62,65,70,88,97,104],"braid":[16,43,67,90],"group":[17,91],"and":[18,36,69,93,121],"Greenberger-Horne-Zeilinger":[20],"(GHZ)":[21],"states.":[22,99],"We":[23,83],"first":[24],"present":[25],"new":[26,41,89],"2-groups":[30,52],"in":[31,117],"terms":[32],"structures":[35],"use":[37],"them":[38],"to":[39,61],"derive":[40],"as":[45],"extensions":[46],"by":[53],"symmetric":[55],"group.":[56],"A":[57],"few":[58],"subtleties":[59],"related":[60],"correspondence":[63],"between":[64],"GHZ":[71,98],"states":[72],"(particularly":[73],"those":[74],"for":[75],"an":[76,111],"odd":[77],"number":[78],"qubits)":[80],"are":[81],"clarified.":[82],"also":[84],"discuss":[85],"Yang\u2013Baxterization":[86],"evolution":[95],"Our":[100],"study":[101],"suggests":[102],"that":[103],"braiding":[106],"quantum":[107,118,123],"gates":[108],"may":[109],"play":[110],"important":[112],"role,":[113],"through":[114],"error":[119],"correction":[120],"topological":[122],"computing.":[124]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}
