{"id":"https://openalex.org/W7225123085","doi":"https://doi.org/10.5281/zenodo.23877249","title":"Majorana Braiding Generates Single-Qubit Clifford Group of Order 24 \u2014 E8 Intelligence Research","display_name":"Majorana Braiding Generates Single-Qubit Clifford Group of Order 24 \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225123085","doi":"https://doi.org/10.5281/zenodo.23877249"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23877249","doi":"https://doi.org/10.5281/zenodo.23877249","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23877249","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23877249","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153285007","display_name":"Andrew Stewart Caldin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Caldin, Andrew Stewart","raw_affiliation_strings":["Independent Researcher, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153285007"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.8003000020980835,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.8003000020980835,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.029999999329447746,"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":0.025200000032782555,"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/majorana-zero-modes","display_name":"Majorana zero modes","score":0.996999979019165},{"id":"https://openalex.org/keywords/non-abelian-anyons","display_name":"non-Abelian anyons","score":0.9380000233650208},{"id":"https://openalex.org/keywords/majorana-braiding","display_name":"Majorana braiding","score":0.8379999995231628},{"id":"https://openalex.org/keywords/clifford-group","display_name":"Clifford group","score":0.8119999766349792},{"id":"https://openalex.org/keywords/binary-tetrahedral-group","display_name":"binary tetrahedral group","score":0.9710000157356262},{"id":"https://openalex.org/keywords/braid-groups","display_name":"braid groups","score":0.7179999947547913},{"id":"https://openalex.org/keywords/ising-anyons","display_name":"Ising anyons","score":0.7850000262260437},{"id":"https://openalex.org/keywords/r-matrix","display_name":"R-matrix","score":0.7870000004768372},{"id":"https://openalex.org/keywords/e8","display_name":"E8","score":0.5440000295639038},{"id":"https://openalex.org/keywords/topological-quantum-computation","display_name":"topological quantum computation","score":0.5720000267028809}],"concepts":[{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.7781000137329102},{"id":"https://openalex.org/C2778761060","wikidata":"https://www.wikidata.org/wiki/Q6714234","display_name":"MAJORANA","level":3,"score":0.6908000111579895},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6315000057220459},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.6274999976158142},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.6144000291824341},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5924999713897705},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5476999878883362},{"id":"https://openalex.org/C187483380","wikidata":"https://www.wikidata.org/wiki/Q7825042","display_name":"Topological quantum computer","level":3,"score":0.45669999718666077},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43709999322891235},{"id":"https://openalex.org/C2777446375","wikidata":"https://www.wikidata.org/wiki/Q5528","display_name":"Anyon","level":4,"score":0.412200003862381},{"id":"https://openalex.org/C3168419","wikidata":"https://www.wikidata.org/wiki/Q280222","display_name":"Tetrahedral symmetry","level":3,"score":0.39980000257492065},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3955000042915344},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3700999915599823},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.3675999939441681},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.3619000017642975},{"id":"https://openalex.org/C45969854","wikidata":"https://www.wikidata.org/wiki/Q2727849","display_name":"Majorana equation","level":5,"score":0.35760000348091125},{"id":"https://openalex.org/C147441545","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid theory","level":3,"score":0.3418000042438507},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C83716740","wikidata":"https://www.wikidata.org/wiki/Q17104294","display_name":"Triality","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29249998927116394},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2709999978542328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26100000739097595},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C207570611","wikidata":"https://www.wikidata.org/wiki/Q1256500","display_name":"Rotation group SO","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23877249","doi":"https://doi.org/10.5281/zenodo.23877249","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23877249","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23877250","doi":"https://doi.org/10.5281/zenodo.23877250","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23877250","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23877249","doi":"https://doi.org/10.5281/zenodo.23877249","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23877249","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7224799730","https://openalex.org/W7222923426","https://openalex.org/W7204121009","https://openalex.org/W7211942030","https://openalex.org/W7223557745","https://openalex.org/W7204035874","https://openalex.org/W7168238486","https://openalex.org/W2620302808","https://openalex.org/W2900649839","https://openalex.org/W7208711974"],"abstract_inverted_index":{"FINDING:":[0],"Majorana":[1,44],"zero":[2],"modes":[3],"realize":[4],"non-Abelian":[5],"anyons":[6],"whose":[7],"braiding":[8],"generates":[9],"a":[10],"finite":[11],"subgroup":[12],"of":[13,23,99,107,143,181],"the":[14,19,28,104,182],"Clifford":[15,21,51,78],"group":[16,22,31,52,75,102],"\u2014":[17],"specifically":[18],"single-qubit":[20,50],"order":[24,63,98,112,148],"24,":[25],"isomorphic":[26],"to":[27,129,169],"binary":[29,71,100],"tetrahedral":[30,72,101],"2T.":[32],"|":[33,94],"MATH:":[34],"Braiding":[35],"operators":[36],"B_ij":[37],"=":[38,48,54,56,66,68,70,86,97,115,124,132,134,139,141,162,164,166],"exp(\u03c0":[39],"\u03b3_i":[40],"\u03b3_j":[41],"/":[42],"4);":[43],"algebra":[45],"{\u03b3_i,":[46],"\u03b3_j}":[47],"2\u03b4_ij;":[49],"|C\u2081|":[53],"24":[55,65,96,131,138],"2\u00b3\u00b73;":[57],"2T":[58,127,150],"\u2245":[59],"SL(2,3)":[60],"\u2282":[61,151],"SU(2),":[62],"24;":[64,149],"4!":[67,140],"2\u00b712":[69,133],"order;":[73],"braid":[74,157],"B_n":[76],"\u2192":[77,122],"via":[79],"Burau/Ising":[80],"representation;":[81],"Ising":[82],"anyon":[83],"fusion":[84],"\u03c3\u00d7\u03c3":[85],"1+\u03c8;":[87],"R-matrix":[88],"eigenvalues":[89],"e^{\u00b1i\u03c0/8}":[90],"(silver":[91],"ratio":[92],"phase).":[93],"CONNECTION:":[95],"2T,":[103],"double":[105],"cover":[106],"A\u2084":[108],"(tetrahedral":[109],"rotation":[110],"group,":[111],"12).":[113],"Tetrahedron":[114],"4":[116,120,144],"vertices,":[117],"6":[118],"edges,":[119],"faces":[121],"4+6+4":[123],"14,":[125],"but":[126],"doubles":[128],"24.":[130],"2\u00b7(tetrahedral":[135],"rotations).":[136],"Also":[137],"permutations":[142],"elements":[145],"(S\u2084":[146],"has":[147,160],"S\u2084":[152],"as":[153],"normal":[154],"subgroup).":[155],"The":[156],"phase":[158],"e^{i\u03c0/8}":[159],"|phase|":[161],"\u03c0/8":[163],"22.5\u00b0":[165],"360\u00b0/16,":[167],"linking":[168],"16-fold":[170],"symmetry":[171],"(":[172],"Author:":[173],"Andrew":[174],"Stewart":[175],"Caldin,":[176],"Independent":[177],"Researcher,":[178],"UK.":[179],"Part":[180],"E8":[183],"Intelligence":[184],"Research":[185],"series.":[186],"Platform:":[187],"e8intelligence.com":[188]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-11-03T00:00:00"}