{"id":"https://openalex.org/W101860259","doi":null,"title":"QUANTUM ERROR CORRECTION WITHOUT MEASUREMENT AND AN EFFICIENT RECOVERY OPERATION","display_name":"QUANTUM ERROR CORRECTION WITHOUT MEASUREMENT AND AN EFFICIENT RECOVERY OPERATION","publication_year":2011,"publication_date":"2011-02-08","ids":{"openalex":"https://openalex.org/W101860259","mag":"101860259"},"language":"en","primary_location":{"id":"mag:101860259","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1102.1618","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/1102.1618","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102931711","display_name":"Chi-Kwong Li","orcid":"https://orcid.org/0000-0002-4825-6270","observed_orcids":["https://orcid.org/0000-0002-4825-6270"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chi-Kwong Li","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4825-6270","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012723994","display_name":"Mikio Nakahara","orcid":"https://orcid.org/0000-0001-5219-9398","observed_orcids":["https://orcid.org/0000-0001-5219-9398"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mikio Nakahara","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5219-9398","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009190519","display_name":"Yiu\u2010Tung Poon","orcid":"https://orcid.org/0000-0002-5171-0446","observed_orcids":["https://orcid.org/0000-0002-5171-0446"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yiu\u2010Tung Poon","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5171-0446","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039570844","display_name":"Nung-Sing Sze","orcid":"https://orcid.org/0000-0003-1567-2654","observed_orcids":["https://orcid.org/0000-0003-1567-2654"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nung-Sing Sze","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1567-2654","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017623051","display_name":"Hiroyuki Tomita","orcid":"https://orcid.org/0000-0002-3291-0274","observed_orcids":["https://orcid.org/0000-0002-3291-0274"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hiroyuki Tomita","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3291-0274","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":1,"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":0.9789999723434448,"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":0.9789999723434448,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.01889999955892563,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.00039999998989515007,"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/quantum-error-correction","display_name":"quantum error correction","score":0.9660000205039978},{"id":"https://openalex.org/keywords/quantum-channels","display_name":"quantum channels","score":0.5839999914169312},{"id":"https://openalex.org/keywords/decoherence","display_name":"decoherence","score":0.7310000061988831},{"id":"https://openalex.org/keywords/ancilla-qubits","display_name":"ancilla qubits","score":0.652999997138977},{"id":"https://openalex.org/keywords/syndrome-measurement","display_name":"syndrome measurement","score":0.781000018119812},{"id":"https://openalex.org/keywords/partial-trace","display_name":"partial trace","score":0.6710000038146973},{"id":"https://openalex.org/keywords/decoding","display_name":"decoding","score":0.36000001430511475},{"id":"https://openalex.org/keywords/tensor-product-states","display_name":"tensor product states","score":0.5370000004768372}],"concepts":[{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.6616449356079102},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6095693111419678},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.5828973054885864},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.5641852617263794},{"id":"https://openalex.org/C122527463","wikidata":"https://www.wikidata.org/wiki/Q578430","display_name":"Quantum decoherence","level":3,"score":0.541292130947113},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5211023092269897},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.4967692494392395},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.49555957317352295},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.4906562864780426},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4847135543823242},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4599859118461609},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4554431736469269},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.42183834314346313},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4183042347431183},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3864032030105591},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3408013582229614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25853800773620605},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25539135932922363},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.23183801770210266},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:101860259","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1102.1618","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:101860259","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1102.1618","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":4,"referenced_works":["https://openalex.org/W1530995657","https://openalex.org/W2001597543","https://openalex.org/W2990961515","https://openalex.org/W3043191710"],"related_works":["https://openalex.org/W2132432289","https://openalex.org/W7096222855","https://openalex.org/W2133231682","https://openalex.org/W1679069470","https://openalex.org/W2594128903","https://openalex.org/W7098064624","https://openalex.org/W2060887750","https://openalex.org/W2054633995","https://openalex.org/W4394649137","https://openalex.org/W2471581415"],"abstract_inverted_index":{"1.":[0],"IntroductionQuantum":[1],"system":[2],"is":[3,40,98,128,175,195,206,224,267,322],"vulnerable":[4],"to":[5,19,23,51,207,213,318,324],"disturbance":[6],"from":[7],"the":[8,15,43,68,82,100,106,119,132,172,192,209,231,265,273,280],"external":[9],"environment,":[10],"which":[11,149,230],"leads":[12],"todecoherence":[13],"in":[14,88,103,118,131,137,148,198,211,283,301],"system.":[16],"We":[17,217,271,286],"have":[18,84],"overcome":[20],"this":[21,204],"di\ufb03culty":[22],"realize":[24],"a":[25,29,76,125,167,176,178,225,234,246,248,254,259,294,298],"working":[26],"quanutumcomputer":[27],"and":[28,154,171,181,241],"dependable":[30],"quantum":[31,72,92,142,215,221],"information":[32,93],"processing.":[33],"Quantum":[34],"error":[35,64,73],"correction":[36,74,312],"(QEC)[1,":[37],"2,":[38],"3]":[39],"one":[41,59],"of":[42,124,203,237,264,276,297],"most":[44],"promising":[45],"candidates":[46],"for":[47,140,219,313],"overcoming":[48],"decoherence.QEC":[49],"proposals":[50],"date":[52],"are":[53,164],"separated":[54],"roughly":[55],"into":[56,166],"two":[57],"classes,":[58],"employs":[60],"extra":[61],"ancilla":[62,114,183,243],"qubitsfor":[63],"syndrome":[65,107],"readout":[66],"while":[67,122],"other,":[69],"called":[70],"operator":[71],"(OQEC)employs":[75],"higher":[77],"rank":[78],"projection":[79,156,193],"operator.":[80],"However,":[81],"schemes":[83],"not":[85],"been":[86],"built":[87,197],"actualquantum":[89],"computing":[90],"or":[91],"processing":[94,117],"so":[95],"far.":[96],"This":[97],"dueto":[99],"following":[101],"obstaclesinherent":[102],"these":[104],"QECs;":[105],"must":[108],"be":[109,309],"read":[110],"out":[111],"by":[112,253,258],"introducing":[113],"qubits":[115],"duringcomputing/information":[116],"former":[120],"case,":[121],"realization":[123],"high-rank":[126],"projectionoperator":[127],"physically":[129],"challenging":[130],"latter":[133],"case.It":[134],"was":[135],"shown":[136],"[4]":[138,212],"that":[139,304],"some":[141],"channels":[143,316],"there":[144,223],"exist":[145],"di\ufb00erent":[146],"QECs":[147],"nosyndrome":[150],"measurements,":[151],"no":[152,155],"ancillas":[153],"operators":[157],"were":[158],"required.":[159],"Recovery":[160],"operationand":[161],"decoding":[162,249],"operation":[163,170,194],"combined":[165],"single":[168],"unitary":[169,226,255],"output":[173,200,232],"state":[174,186,240],"directproductof":[177],"decoded":[179,238],"qubitstate":[180],"an":[182,242],"state.":[184,244],"Aqubit":[185],"isreproducedwithout":[187],"recoveringthe":[188],"codeword":[189],"and,":[190],"moreover,":[191],"automatically":[196],"our":[199,292,305],"state.The":[201],"purpose":[202],"paper":[205,266],"extend":[208],"results":[210],"general":[214],"channels.":[216],"showthat":[218],"any":[220],"channel":[222,307],"recovery":[227,306],"operation,":[228],"with":[229],"stateis":[233],"tensor":[235],"product":[236],"qubit":[239],"As":[245],"result,":[247],"scheme":[250],"canbe":[251],"done":[252],"gate":[256],"followed":[257],"partial":[260],"trace":[261],"operation.The":[262],"rest":[263],"organized":[268],"as":[269],"follows.":[270],"introduce":[272],"basic":[274],"notions":[275],"OQEC":[277],"andthen":[278],"prove":[279],"main":[281],"theorem":[282,299],"Section":[284,320],"2.":[285],"also":[287],"give":[288],"simple":[289],"examples":[290],"demonstrating":[291],"resultand":[293],"simpli\ufb01ed":[295],"proof":[296],"given":[300],"[2]":[302],"illustrating":[303],"can":[308],"usedto":[310],"do":[311],"many":[314],"other":[315],"related":[317],"ours.":[319],"3":[321],"devoted":[323],"summary":[325],"anddiscussions.":[326]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2016-06-24T00:00:00"}