{"id":"https://openalex.org/W2152038389","doi":"https://doi.org/10.1109/tit.2014.2303801","title":"Fidelity Lower Bounds for Stabilizer and CSS Quantum Codes","display_name":"Fidelity Lower Bounds for Stabilizer and CSS Quantum Codes","publication_year":2014,"publication_date":"2014-03-11","ids":{"openalex":"https://openalex.org/W2152038389","doi":"https://doi.org/10.1109/tit.2014.2303801","mag":"2152038389"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2303801","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2303801","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088515682","display_name":"Alexei Ashikhmin","orcid":"https://orcid.org/0000-0002-7016-1614"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexei Ashikhmin","raw_affiliation_strings":["Bell Laboratories, Alcatel-Lucent Inc., Murray Hill, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Alcatel-Lucent Inc., Murray Hill, NJ, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088515682"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.409,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.75514634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"60","issue":"6","first_page":"3104","last_page":"3116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9995999932289124,"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":0.9995999932289124,"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/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/fidelity","display_name":"Fidelity","score":0.6854329109191895},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6255202889442444},{"id":"https://openalex.org/keywords/stabilizer","display_name":"Stabilizer (aeronautics)","score":0.525579035282135},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5022311210632324},{"id":"https://openalex.org/keywords/quantum-convolutional-code","display_name":"Quantum convolutional code","score":0.4593847393989563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42674803733825684},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42652595043182373},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.42466920614242554},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4239479899406433},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39890486001968384},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.3065422773361206},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25918060541152954},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.2220536768436432},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.19432643055915833},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16295301914215088},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.14257314801216125},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.11394244432449341},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06954041123390198},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.054149359464645386}],"concepts":[{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.6854329109191895},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6255202889442444},{"id":"https://openalex.org/C2777502316","wikidata":"https://www.wikidata.org/wiki/Q2712515","display_name":"Stabilizer (aeronautics)","level":2,"score":0.525579035282135},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5022311210632324},{"id":"https://openalex.org/C69497775","wikidata":"https://www.wikidata.org/wiki/Q7269025","display_name":"Quantum convolutional code","level":5,"score":0.4593847393989563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42674803733825684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42652595043182373},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.42466920614242554},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4239479899406433},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39890486001968384},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.3065422773361206},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25918060541152954},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2220536768436432},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.19432643055915833},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16295301914215088},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.14257314801216125},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.11394244432449341},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06954041123390198},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.054149359464645386},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2014.2303801","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2303801","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1593683169","https://openalex.org/W1606480398","https://openalex.org/W1631356911","https://openalex.org/W2021404493","https://openalex.org/W2042474962","https://openalex.org/W2063592138","https://openalex.org/W2069711632","https://openalex.org/W2098666392","https://openalex.org/W2106864314","https://openalex.org/W2111937453","https://openalex.org/W2114207424","https://openalex.org/W2118776409","https://openalex.org/W2131690084","https://openalex.org/W2143438504","https://openalex.org/W2144045978","https://openalex.org/W2163386460","https://openalex.org/W2167413626","https://openalex.org/W2490759781","https://openalex.org/W2764347725","https://openalex.org/W2964196967","https://openalex.org/W3100206575"],"related_works":["https://openalex.org/W2153823223","https://openalex.org/W2048984244","https://openalex.org/W2142613177","https://openalex.org/W2048831762","https://openalex.org/W2560119569","https://openalex.org/W2138014387","https://openalex.org/W2566064824","https://openalex.org/W2020314309","https://openalex.org/W2134039451","https://openalex.org/W3082966133"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,13,30,83,105],"estimate":[4],"the":[5,19,32,37,48,57,66,71,88,92],"fidelity":[6,20,59,67,85,112,138],"of":[7,21,36,39,60,74,77,115,137],"stabilizer":[8,23,42,78,130,171],"and":[9,43,79,139,148],"CSS":[10,44,80,146,151,156,162],"codes.":[11,45,81,157,172],"First,":[12],"derive":[14,84],"a":[15,22,110,116,128,144,165],"lower":[16,54],"bound":[17],"on":[18,56],"code":[24,93,103,131,140],"via":[25],"its":[26],"quantum":[27,34,50,72],"enumerator.":[28],"Next,":[29],"find":[31],"average":[33,49,58],"enumerators":[35,51,73],"ensembles":[38,76],"finite":[40],"length":[41,94],"We":[46,63],"use":[47],"for":[52,108],"obtaining":[53],"bounds":[55,68,86],"these":[61],"ensembles.":[62],"further":[64],"improve":[65],"by":[69],"estimating":[70],"expurgated":[75],"Finally,":[82],"in":[87,124,135],"asymptotic":[89],"regime":[90],"when":[91],"tends":[95],"to":[96],"infinity.":[97],"These":[98],"results":[99,120,159],"tell":[100],"us":[101],"which":[102],"rate":[104],"can":[106],"afford":[107],"achieving":[109],"target":[111],"with":[113,143,170],"codes":[114,152,163],"given":[117],"length.":[118],"The":[119],"also":[121],"show":[122],"that":[123,149,161],"symmetric":[125],"depolarizing":[126],"channel":[127],"typical":[129,145],"has":[132],"better":[133],"performance,":[134],"terms":[136],"rate,":[141],"compared":[142,169],"codes,":[147],"balanced":[150],"significantly":[153],"outperform":[154],"other":[155],"Asymptotic":[158],"demonstrate":[160],"have":[164],"fundamental":[166],"performance":[167],"loss":[168]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}