{"id":"https://openalex.org/W4293187836","doi":"https://doi.org/10.22331/q-2022-04-27-698","title":"The XYZ<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi/><mml:mn>2</mml:mn></mml:msup></mml:math> hexagonal stabilizer code","display_name":"The XYZ<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi/><mml:mn>2</mml:mn></mml:msup></mml:math> hexagonal stabilizer code","publication_year":2022,"publication_date":"2022-04-27","ids":{"openalex":"https://openalex.org/W4293187836","doi":"https://doi.org/10.22331/q-2022-04-27-698"},"language":"lv","primary_location":{"id":"doi:10.22331/q-2022-04-27-698","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-27-698","pdf_url":"https://quantum-journal.org/papers/q-2022-04-27-698/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2022-04-27-698/pdf/","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069586327","display_name":"Basudha Srivastava","orcid":"https://orcid.org/0000-0002-4972-4216"},"institutions":[{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Basudha Srivastava","raw_affiliation_strings":["Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-4972-4216","affiliations":[{"raw_affiliation_string":"Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden","institution_ids":["https://openalex.org/I881427289"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059455535","display_name":"Anton Frisk Kockum","orcid":"https://orcid.org/0000-0002-2534-3021"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Anton Frisk Kockum","raw_affiliation_strings":["Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Gothenburg, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-2534-3021","affiliations":[{"raw_affiliation_string":"Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002881429","display_name":"Mats Granath","orcid":"https://orcid.org/0000-0003-3185-2014"},"institutions":[{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Mats Granath","raw_affiliation_strings":["Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden"],"raw_orcid":"https://orcid.org/0000-0003-3185-2014","affiliations":[{"raw_affiliation_string":"Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden","institution_ids":["https://openalex.org/I881427289"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":4.4323,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.95430108,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"6","issue":null,"first_page":"698","last_page":"698"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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":0.9948999881744385,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9825999736785889,"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":0.41218629479408264},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30872446298599243}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41218629479408264},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30872446298599243}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.22331/q-2022-04-27-698","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-27-698","pdf_url":"https://quantum-journal.org/papers/q-2022-04-27-698/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"}],"best_oa_location":{"id":"doi:10.22331/q-2022-04-27-698","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-27-698","pdf_url":"https://quantum-journal.org/papers/q-2022-04-27-698/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":[{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"},{"id":"https://openalex.org/F4320336501","display_name":"Wallenberg Centre for Molecular and Translational Medicine","ror":null},{"id":"https://openalex.org/F4320336997","display_name":"Wallenberg Center for Quantum Technology, Chalmers University of Technology","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4293187836.pdf","grobid_xml":"https://content.openalex.org/works/W4293187836.grobid-xml"},"referenced_works_count":78,"referenced_works":["https://openalex.org/W1521207535","https://openalex.org/W1656481297","https://openalex.org/W1968446563","https://openalex.org/W1984021697","https://openalex.org/W1995611441","https://openalex.org/W1999706070","https://openalex.org/W2002583548","https://openalex.org/W2012317289","https://openalex.org/W2014633300","https://openalex.org/W2026181396","https://openalex.org/W2030867075","https://openalex.org/W2042474962","https://openalex.org/W2045176588","https://openalex.org/W2054426168","https://openalex.org/W2056281570","https://openalex.org/W2071636337","https://openalex.org/W2075431083","https://openalex.org/W2088636071","https://openalex.org/W2089540019","https://openalex.org/W2095025840","https://openalex.org/W2099939664","https://openalex.org/W2107038224","https://openalex.org/W2109785828","https://openalex.org/W2135273380","https://openalex.org/W2140970025","https://openalex.org/W2141708961","https://openalex.org/W2157276712","https://openalex.org/W2167927798","https://openalex.org/W2174510006","https://openalex.org/W2530095757","https://openalex.org/W2580762073","https://openalex.org/W2610870949","https://openalex.org/W2611085468","https://openalex.org/W2619719596","https://openalex.org/W2750849968","https://openalex.org/W2751086103","https://openalex.org/W2781738013","https://openalex.org/W2841500134","https://openalex.org/W2889126882","https://openalex.org/W2905125220","https://openalex.org/W2990961515","https://openalex.org/W2999629616","https://openalex.org/W3022429210","https://openalex.org/W3033497438","https://openalex.org/W3033912009","https://openalex.org/W3037443854","https://openalex.org/W3085306040","https://openalex.org/W3094595762","https://openalex.org/W3098424936","https://openalex.org/W3100736866","https://openalex.org/W3100931082","https://openalex.org/W3100973904","https://openalex.org/W3104703121","https://openalex.org/W3105040923","https://openalex.org/W3111162498","https://openalex.org/W3112808256","https://openalex.org/W3119028457","https://openalex.org/W3125185787","https://openalex.org/W3125949256","https://openalex.org/W3155795538","https://openalex.org/W3178633198","https://openalex.org/W3181439919","https://openalex.org/W3181660950","https://openalex.org/W3184667711","https://openalex.org/W3194025247","https://openalex.org/W3199789432","https://openalex.org/W3202233822","https://openalex.org/W3203972939","https://openalex.org/W3205751967","https://openalex.org/W3216031933","https://openalex.org/W3216176305","https://openalex.org/W4200632123","https://openalex.org/W4225259930","https://openalex.org/W4225797040","https://openalex.org/W4225926379","https://openalex.org/W4226374459","https://openalex.org/W4281479206","https://openalex.org/W4394672652"],"related_works":["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","https://openalex.org/W2600246793"],"abstract_inverted_index":{"We":[0,88],"consider":[1],"a":[2,7,25,29,44,64,122],"topological":[3],"stabilizer":[4,100],"code":[5,15,74,94,132,139,151,189],"on":[6,63],"honeycomb":[8,21],"grid,":[9],"the":[10,19,48,82,90,93,116,129,134,150,177,201,205],"\"XYZ<mml:math":[11],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi/><mml:mn>2</mml:mn></mml:msup></mml:math>\"":[12],"code.":[13],"The":[14,188],"is":[16,24,153],"inspired":[17],"by":[18,33],"Kitaev":[20],"model":[22],"and":[23,57,133,161],"simple":[26],"realization":[27],"of":[28,47,69,92,124,197,204],"\"matching":[30],"code\"":[31],"discussed":[32],"Wootton":[34],"[J.":[35],"Phys.":[36],"A:":[37],"Math.":[38],"Theor.":[39],"48,":[40],"215302":[41],"(2015)],":[42],"with":[43,78,169,181,194],"specific":[45],"implementation":[46],"boundary.":[49],"It":[50],"utilizes":[51],"weight-six":[52],"(<mml:math":[53,59],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>X</mml:mi><mml:mi>Y</mml:mi><mml:mi>Z</mml:mi><mml:mi>X</mml:mi><mml:mi>Y</mml:mi><mml:mi>Z</mml:mi></mml:math>)":[54],"plaquette":[55,198],"stabilizers":[56,62,80],"weight-two":[58],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>X</mml:mi><mml:mi>X</mml:mi></mml:math>)":[60],"link":[61],"planar":[65],"hexagonal":[66],"grid":[67],"composed":[68],"<mml:math":[70,76,104,106,109,141,146,154,159,163,171],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mn>2</mml:mn><mml:msup><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>":[71,155],"qubits":[72],"for":[73,115,144,156,167,208,215],"distance":[75,140,152],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>d</mml:mi></mml:math>,":[77],"weight-three":[79],"at":[81],"boundary,":[83],"stabilizing":[84],"one":[85],"logical":[86,117,185],"qubit.":[87],"study":[89],"properties":[91,193],"using":[95],"maximum-likelihood":[96],"decoding,":[97],"assuming":[98],"perfect":[99],"measurements.":[101],"For":[102],"pure":[103,145,158,162],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>X</mml:mi></mml:math>,":[105],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>Y</mml:mi></mml:math>,":[107],"or":[108,218],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>Z</mml:mi></mml:math>":[110,160,172],"noise,":[111,148],"we":[112],"can":[113],"solve":[114],"failure":[118,186],"rate":[119],"analytically,":[120],"giving":[121],"threshold":[123],"50%.":[125],"In":[126],"contrast":[127],"to":[128,176],"rotated":[130],"surface":[131],"XZZX":[135,178],"code,":[136,179],"which":[137,211],"have":[138],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>":[142],"only":[143],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>Y</mml:mi></mml:math>":[147,164],"here":[149],"both":[157],"noise.":[165],"Thresholds":[166],"noise":[168],"finite":[170],"bias":[173],"are":[174],"similar":[175],"but":[180],"markedly":[182],"lower":[183],"sub-threshold":[184],"rates.":[187],"possesses":[190],"distinctive":[191],"syndrome":[192],"unidirectional":[195],"pairs":[196],"defects":[199],"along":[200],"three":[202],"directions":[203],"triangular":[206],"lattice":[207],"isolated":[209],"errors,":[210],"may":[212],"be":[213],"useful":[214],"efficient":[216],"matching-based":[217],"other":[219],"approximate":[220],"decoding.":[221]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2022-08-27T00:00:00"}
