{"id":"https://openalex.org/W2916363163","doi":"https://doi.org/10.22331/q-2020-03-23-245","title":"Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames","display_name":"Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames","publication_year":2020,"publication_date":"2020-03-23","ids":{"openalex":"https://openalex.org/W2916363163","doi":"https://doi.org/10.22331/q-2020-03-23-245","mag":"2916363163"},"language":"en","primary_location":{"id":"doi:10.22331/q-2020-03-23-245","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-03-23-245","pdf_url":"https://quantum-journal.org/papers/q-2020-03-23-245/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","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2020-03-23-245/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063563589","display_name":"Mischa P. Woods","orcid":"https://orcid.org/0000-0002-0547-4569"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Mischa P. Woods","raw_affiliation_strings":["Institute for Theoretical Physics, ETH Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085188489","display_name":"\u00c1lvaro M. Alhambra","orcid":"https://orcid.org/0000-0002-5889-4022"},"institutions":[{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"\u00c1lvaro M. Alhambra","raw_affiliation_strings":["Perimeter Institute for Theoretical Physics, Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics, Waterloo, Canada","institution_ids":["https://openalex.org/I183974707"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063563589"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":5.1649,"has_fulltext":true,"cited_by_count":50,"citation_normalized_percentile":{"value":0.96182852,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"4","issue":null,"first_page":"245","last_page":"245"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9998999834060669,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9998999834060669,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"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":0.9987000226974487,"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/algorithm","display_name":"Algorithm","score":0.5995070934295654},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44870343804359436},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4178040027618408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33738815784454346},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18042725324630737}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5995070934295654},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44870343804359436},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4178040027618408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33738815784454346},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18042725324630737}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2020-03-23-245","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-03-23-245","pdf_url":"https://quantum-journal.org/papers/q-2020-03-23-245/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:1902.07725","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.07725","pdf_url":"https://arxiv.org/pdf/1902.07725","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:c03192554d8e4478858ff7858385524c","is_oa":true,"landing_page_url":"https://doaj.org/article/c03192554d8e4478858ff7858385524c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 245 (2020)","raw_type":"article"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/411156","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/411156","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, 4","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.3929/ethz-b-000411156","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000411156","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.22331/q-2020-03-23-245","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-03-23-245","pdf_url":"https://quantum-journal.org/papers/q-2020-03-23-245/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":[{"id":"https://openalex.org/G165152779","display_name":"The resource of time in quantum information theory","funder_award_id":"179914","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4430097687","display_name":null,"funder_award_id":"PZ00P2","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4621158401","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4999133074","display_name":null,"funder_award_id":"PZ00P2_179914","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5729343713","display_name":null,"funder_award_id":"PZ00P2_17991","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8029063489","display_name":null,"funder_award_id":"PZ00P2 179914","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320321012","display_name":"Technische Universiteit Delft","ror":"https://ror.org/02e2c7k09"},{"id":"https://openalex.org/F4320331462","display_name":"Institut P\u00e9rim\u00e8tre de physique th\u00e9orique","ror":"https://ror.org/013m0ej23"},{"id":"https://openalex.org/F4320335366","display_name":"National Center of Competence in Research Quantum Science and Technology","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2916363163.pdf","grobid_xml":"https://content.openalex.org/works/W2916363163.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W1517813625","https://openalex.org/W1533024485","https://openalex.org/W1591879484","https://openalex.org/W1759482226","https://openalex.org/W1790859230","https://openalex.org/W1828782323","https://openalex.org/W1971861950","https://openalex.org/W1981983416","https://openalex.org/W2001007246","https://openalex.org/W2011867118","https://openalex.org/W2015718083","https://openalex.org/W2024890519","https://openalex.org/W2025046661","https://openalex.org/W2027678071","https://openalex.org/W2034864060","https://openalex.org/W2043311817","https://openalex.org/W2054620262","https://openalex.org/W2062561656","https://openalex.org/W2063215998","https://openalex.org/W2064185701","https://openalex.org/W2070421562","https://openalex.org/W2072496546","https://openalex.org/W2079294297","https://openalex.org/W2083523039","https://openalex.org/W2094974378","https://openalex.org/W2098838878","https://openalex.org/W2148115906","https://openalex.org/W2169656062","https://openalex.org/W2263744690","https://openalex.org/W2503896999","https://openalex.org/W2520649408","https://openalex.org/W2528596804","https://openalex.org/W2534532550","https://openalex.org/W2582683281","https://openalex.org/W2593013966","https://openalex.org/W2608205557","https://openalex.org/W2622552587","https://openalex.org/W2755111892","https://openalex.org/W2763302490","https://openalex.org/W2765570517","https://openalex.org/W2807226344","https://openalex.org/W2897370229","https://openalex.org/W2898066758","https://openalex.org/W2898842402","https://openalex.org/W2917449642","https://openalex.org/W2962980132","https://openalex.org/W2963760674","https://openalex.org/W2965781426","https://openalex.org/W2994736278","https://openalex.org/W2998454575","https://openalex.org/W3009364745","https://openalex.org/W3037620826","https://openalex.org/W3094688021","https://openalex.org/W3100777706","https://openalex.org/W3102142151","https://openalex.org/W3103021854","https://openalex.org/W3103769813","https://openalex.org/W3104157705","https://openalex.org/W3105292588","https://openalex.org/W3105437228","https://openalex.org/W3130678601","https://openalex.org/W4293581812"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Following":[0],"the":[1,4,54,69,91,97,100,126,129,131,133,136,155,196,200,209,213],"introduction":[2],"of":[3,6,36,52,57,71,76,99,154,162,164],"task":[5],"<mml:math":[7,41],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[8,14],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[9,15],"class=\"MJX-tex-mathit\"":[10,16],"mathvariant=\"italic\">reference":[11],"frame":[12,25],"error</mml:mtext></mml:mrow></mml:math><mml:math":[13],"mathvariant=\"italic\">correction</mml:mtext></mml:mrow></mml:math>":[17],"\\cite{hayden2017error},":[18],"we":[19,47,104,181,202],"show":[20,105,182],"how,":[21],"by":[22,85,187],"using":[23],"reference":[24,165,197],"alignment":[26],"with":[27,96],"clocks,":[28],"one":[29],"can":[30,117,124],"add":[31],"a":[32,50,87,109,160],"continuous":[33],"Abelian":[34],"group":[35,70],"transversal":[37,72],"logical":[38],"gates":[39,73],"to":[40,82,175,184,208],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>y</mml:mi></mml:math>":[42],"error-correcting":[43],"code.":[44],"With":[45],"this":[46,84,115,186],"further":[48],"explore":[49],"way":[51],"circumventing":[53],"no-go":[55,137],"theorem":[56,138],"Eastin":[58],"and":[59,119,135,167,180,212],"Knill,":[60],"which":[61],"states":[62],"that":[63,94,106],"if":[64,142],"local":[65],"errors":[66,176],"are":[67,80],"correctable,":[68],"must":[74],"be":[75,118,140,145],"finite":[77],"order.":[78],"We":[79],"able":[81],"do":[83],"introducing":[86],"small":[88,114],"error":[89,116,156,168,192],"on":[90,195],"decoding":[92],"procedure":[93],"decreases":[95],"dimension":[98],"frames":[101,166],"used.":[102],"Furthermore,":[103],"there":[107],"is":[108,157,172],"direct":[110],"relationship":[111],"between":[112],"how":[113,120,183],"accurate":[121,128],"quantum":[122,149],"clocks":[123],"be:":[125],"more":[127],"clock,":[130],"smaller":[132],"error;":[134],"would":[139],"violated":[141],"time":[143],"could":[144],"measured":[146],"perfectly":[147],"in":[148,206],"mechanics.":[150],"The":[151,170],"asymptotic":[152],"scaling":[153],"studied":[158],"under":[159],"number":[161],"scenarios":[163],"models.":[169],"scheme":[171],"also":[173],"extended":[174],"at":[177],"unknown":[178],"locations,":[179],"achieve":[185],"simple":[188],"majority":[189],"voting":[190],"related":[191],"correction":[193],"schemes":[194],"frames.":[198],"In":[199],"Outlook,":[201],"discuss":[203],"our":[204],"results":[205],"relation":[207],"AdS/CFT":[210],"correspondence":[211],"Page-Wooters":[214],"mechanism.":[215]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}