{"id":"https://openalex.org/W4289713249","doi":"https://doi.org/10.1109/isit50566.2022.9834511","title":"Co-design of CSS Codes and Diagonal Gates","display_name":"Co-design of CSS Codes and Diagonal Gates","publication_year":2022,"publication_date":"2022-06-26","ids":{"openalex":"https://openalex.org/W4289713249","doi":"https://doi.org/10.1109/isit50566.2022.9834511"},"language":"en","primary_location":{"id":"doi:10.1109/isit50566.2022.9834511","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834511","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5023820176","display_name":"Jingzhen Hu","orcid":"https://orcid.org/0000-0002-2699-3966"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jingzhen Hu","raw_affiliation_strings":["Duke University,Department of Mathematics,Durham,USA,NC 27708"],"affiliations":[{"raw_affiliation_string":"Duke University,Department of Mathematics,Durham,USA,NC 27708","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101461788","display_name":"Qingzhong Liang","orcid":"https://orcid.org/0000-0002-5073-9431"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qingzhong Liang","raw_affiliation_strings":["Duke University,Department of Mathematics,Durham,USA,NC 27708"],"affiliations":[{"raw_affiliation_string":"Duke University,Department of Mathematics,Durham,USA,NC 27708","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037795370","display_name":"Robert Calderbank","orcid":"https://orcid.org/0000-0003-2084-9717"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert Calderbank","raw_affiliation_strings":["Duke University,Department of Mathematics,Durham,USA,NC 27708"],"affiliations":[{"raw_affiliation_string":"Duke University,Department of Mathematics,Durham,USA,NC 27708","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023820176"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":0.1046,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.28001272,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1229","last_page":"1234"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"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":1.0,"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":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.998199999332428,"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/diagonal","display_name":"Diagonal","score":0.7662027478218079},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5425101518630981},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5048002004623413},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.461395263671875},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42119771242141724},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.36999082565307617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2616220712661743},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.25431033968925476},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23616284132003784},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.22825205326080322},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06373685598373413}],"concepts":[{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.7662027478218079},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5425101518630981},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5048002004623413},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.461395263671875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42119771242141724},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36999082565307617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2616220712661743},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.25431033968925476},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23616284132003784},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.22825205326080322},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06373685598373413},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit50566.2022.9834511","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834511","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1490521149","https://openalex.org/W1542530597","https://openalex.org/W1656594904","https://openalex.org/W1827451679","https://openalex.org/W1908413158","https://openalex.org/W1929354142","https://openalex.org/W1984436207","https://openalex.org/W2005868823","https://openalex.org/W2012760578","https://openalex.org/W2013738604","https://openalex.org/W2013754283","https://openalex.org/W2063592138","https://openalex.org/W2079294297","https://openalex.org/W2094974378","https://openalex.org/W2114207424","https://openalex.org/W2410653068","https://openalex.org/W2755575243","https://openalex.org/W2900580483","https://openalex.org/W2920312441","https://openalex.org/W2980742961","https://openalex.org/W3046642801","https://openalex.org/W3089424125","https://openalex.org/W3095087884","https://openalex.org/W3098541391","https://openalex.org/W3100704244","https://openalex.org/W3161581056","https://openalex.org/W3198787307","https://openalex.org/W3204079156","https://openalex.org/W3209600147","https://openalex.org/W4290804501","https://openalex.org/W4394672652","https://openalex.org/W6632392208","https://openalex.org/W6765638798","https://openalex.org/W6785318933","https://openalex.org/W6802214034","https://openalex.org/W6803395604","https://openalex.org/W6804894848"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2135584473","https://openalex.org/W2964223869","https://openalex.org/W2792539140","https://openalex.org/W2005808740","https://openalex.org/W2295130398","https://openalex.org/W2064951085","https://openalex.org/W2626141450","https://openalex.org/W2810740133","https://openalex.org/W2064919237"],"abstract_inverted_index":{"The":[0,130,197,283],"challenge":[1],"of":[2,18,32,52,133,165,185,192,200,208,225,270],"quantum":[3,215],"computing":[4,216],"is":[5,27,232,242,260,279,285],"to":[6,28,205,223,234,256,287],"combine":[7],"error":[8],"resilience":[9],"with":[10,221],"universal":[11],"computation.":[12],"There":[13],"are":[14,21,138,171],"many":[15],"finite":[16],"sets":[17],"gates":[19,34,58,247],"that":[20,59,147,176,231,248],"universal,":[22],"and":[23,63,112,157],"a":[24,36,45,50,65,134,148,213,229,280],"standard":[25],"choice":[26],"augment":[29],"the":[30,41,61,97,108,113,126,153,162,177,193,209,226,238,243,245,250,258,275],"set":[31],"Clifford":[33],"by":[35,89,140,266],"non-Clifford":[37,281],"unitary":[38],"such":[39],"as":[40],"T":[42],"gate.":[43,68,196],"Given":[44],"CSS":[46,86,154,251],"code,":[47],"we":[48],"introduce":[49],"method":[51,265],"synthesizing":[53],"all":[54],"possible":[55],"diagonal":[56,131,135,149,190,194],"physical":[57,136,150,195,210,227,246],"preserve":[60,249],"codespace":[62,155,259],"induce":[64],"target":[66,178,239,276],"logical":[67,179,240,277],"We":[69,145,173,262],"denote":[70],"an":[71],"\u301an,":[72],"k":[73,75,80,99],"=":[74],"<inf":[76,81,100,116],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[77,82,101,117,188],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</inf>":[78,118],"\u2212":[79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</inf>":[83,102],",":[84],"d\u301b":[85],"code":[87,105,121,252],"$\\mathcal{C}$":[88],"$\\operatorname{CSS}":[90],"\\left(":[91],"{X,{\\mathcal{C}_2};Z,\\mathcal{C}_1^":[92],"\\bot":[93,123],"}":[94],"\\right)$,":[95],"where":[96],"[n,":[98,114],"]":[103,119],"binary":[104,120,141],"${\\mathcal{C}_2}$":[106,166],"determines":[107,125],"X-stabilizers":[109],"in":[110,128,143,167,290],"$\\mathcal{C}$,":[111],"n\u2212k":[115],"$\\mathcal{C}_1^":[122],"$":[124],"Z-stabilizers":[127],"$\\mathcal{C}$.":[129],"entries":[132,160,191],"gate":[137,151,211,278],"indexed":[139],"vectors":[142],"$\\mathbb{F}_2^n$.":[144],"show":[146,175],"preserves":[152],"if":[156,159],"only":[158,181],"from":[161],"same":[163],"coset":[164],"${\\mathcal{C}_1}$":[168],"(same":[169],"X-logical)":[170],"identical.":[172],"also":[174],"operator":[180,241],"specifies":[182],"${2^{{k_1}}}$":[183],"out":[184],"2":[186],"<sup":[187],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[189],"remaining":[198],"degrees":[199],"freedom":[201],"can":[202],"be":[203],"used":[204],"optimize":[206],"implementation":[207],"within":[212],"particular":[214],"infrastructure.":[217],"This":[218],"encompasses":[219],"optimization":[220],"respect":[222],"locality":[224],"gate,":[228],"criterion":[230],"essential":[233],"fault":[235],"tolerance.":[236],"When":[237],"identity,":[244],"represent":[253],"noise":[254],"operators":[255],"which":[257,274],"oblivious.":[261],"illustrate":[263],"our":[264],"providing":[267],"several":[268],"examples":[269],"code-gate":[271],"pairs":[272],"for":[273],"unitary.":[282],"framework":[284],"extended":[286],"stabilizer":[288],"codes":[289],"https://arxiv.org/abs/2109.13481.":[291]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
