{"id":"https://openalex.org/W7203945023","doi":"https://doi.org/10.48550/arxiv.2608.19094","title":"Realizing Logical Diagonal Gates via Transversal Physical $Z$-Rotations in CSS Codes","display_name":"Realizing Logical Diagonal Gates via Transversal Physical $Z$-Rotations in CSS Codes","publication_year":2026,"publication_date":"2026-08-19","ids":{"openalex":"https://openalex.org/W7203945023","doi":"https://doi.org/10.48550/arxiv.2608.19094"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.19094","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19094","pdf_url":"https://arxiv.org/pdf/2608.19094","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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.19094","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123008958","display_name":"K. Sai Mineesh Reddy","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reddy, K. Sai Mineesh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059452861","display_name":"Navin Kashyap","orcid":"https://orcid.org/0000-0001-8834-0082","observed_orcids":["https://orcid.org/0000-0001-8834-0082"]},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kashyap, Navin","raw_affiliation_strings":["Dept. Electrical Communication Engineering , Indian Institute of Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. Electrical Communication Engineering , Indian Institute of Science","institution_ids":["https://openalex.org/I59270414"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9976000189781189,"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":0.9976000189781189,"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":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.0005000000237487257,"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/calderbank-shor-steane-codes","display_name":"Calderbank-Shor-Steane codes","score":0.9309999942779541},{"id":"https://openalex.org/keywords/fault-tolerant-quantum-computation","display_name":"fault-tolerant quantum computing","score":0.7250000238418579},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"minimum distance","score":0.45899999141693115}],"concepts":[{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.8427000045776367},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.666700005531311},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6230000257492065},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42980000376701355},{"id":"https://openalex.org/C21847791","wikidata":"https://www.wikidata.org/wiki/Q191081","display_name":"Logical conjunction","level":2,"score":0.41110000014305115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.392300009727478},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.349700003862381},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.3158999979496002},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28999999165534973},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28049999475479126},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C70992990","wikidata":"https://www.wikidata.org/wiki/Q1681587","display_name":"Systematic code","level":4,"score":0.26589998602867126},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.19094","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19094","pdf_url":"https://arxiv.org/pdf/2608.19094","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.19094","doi":"https://doi.org/10.48550/arxiv.2608.19094","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.19094","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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.19094","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19094","pdf_url":"https://arxiv.org/pdf/2608.19094","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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306227","display_name":"Arthritis National Research Foundation","ror":"https://ror.org/03abbex33"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203945023.pdf","grobid_xml":"https://content.openalex.org/works/W7203945023.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7130236610","https://openalex.org/W7124157012","https://openalex.org/W2980742961","https://openalex.org/W4289713249","https://openalex.org/W7126207234","https://openalex.org/W6929285986","https://openalex.org/W7202254545","https://openalex.org/W4415401457","https://openalex.org/W7171827471","https://openalex.org/W7140364957"],"abstract_inverted_index":{"Calderbank-Shor-Steane":[0],"(CSS)":[1],"codes,":[2],"constructed":[3],"from":[4],"nested":[5,32],"classical":[6],"codes":[7,39,63],"$C_2":[8],"\\subseteq":[9],"C_1$,":[10],"are":[11],"typically":[12],"optimized":[13],"for":[14,229],"good":[15],"code":[16,94,119,161,169,173,207,213,252],"parameters.":[17],"However,":[18],"practical":[19],"quantum":[20],"computing":[21],"equally":[22],"demands":[23],"fault-tolerant":[24,217],"logical":[25,43,67,99,129,151,222,242,258],"gates.":[26],"In":[27,50],"this":[28,230],"work,":[29],"we":[30,53,82,202,249],"characterize":[31],"pairs":[33],"$(C_1,":[34],"C_2)$":[35],"whose":[36],"resulting":[37],"CSS":[38,62,93,118,172,206,212,251],"realize":[40,65,256],"a":[41,55,97,138,177,211],"target":[42,98,128,241],"diagonal":[44],"gate":[45,130,152],"via":[46,74,154],"transversal":[47,75,141,155],"physical":[48,76,112,140,147,156,234],"$Z$-rotations.":[49,77,223,262],"doing":[51],"so,":[52],"recover":[54],"result":[56],"of":[57,219,240],"Camps-Moreno":[58],"et":[59],"al.":[60],"that":[61,87,215,254],"can":[64,185,203],"only":[66],"single-qubit":[68,259],"$Z$-rotations":[69,73,157],"and":[70,96,105,125,260],"multi-qubit":[71],"controlled":[72,187],"Building":[78],"on":[79],"our":[80,247],"characterization,":[81],"develop":[83],"the":[84,144,159,167,183,189,194,199,232,238],"''appending":[85],"construction'',":[86],"takes":[88],"as":[89,237],"input":[90,160],"an":[91,116],"$[[n',k']]$":[92],"$Q'$":[95,107,162,208],"$Z$-rotation":[100,142],"(single-qubit":[101],"or":[102],"multi-controlled)":[103],"$U_L$,":[104],"extends":[106],"by":[108,136],"systematically":[109],"appending":[110,200],"$n''$":[111,145],"qubits":[113],"to":[114,143,209,226],"obtain":[115,210],"$[[n,k]]$":[117],"$Q$":[120,135,174,214],"with":[121],"$n":[122],"=":[123],"n'+n''$":[124],"$k=k'$.":[126],"The":[127,171,224],"$U_L$":[131],"is":[132,231],"realized":[133,153],"in":[134,158,166,179,193],"applying":[137,198],"well-chosen":[139],"appended":[146],"qubits.":[148],"Moreover,":[149],"any":[150,205],"remains":[163],"transversally":[164,255],"realizable":[165],"extended":[168],"$Q$.":[170],"may":[175],"incur":[176],"loss":[178,184],"minimum":[180],"distance,":[181],"but":[182],"be":[186,227],"through":[188],"parameter":[190],"choices":[191],"made":[192],"construction.":[195],"By":[196],"repeatedly":[197],"construction,":[201],"extend":[204],"supports":[216],"implementations":[218],"multiple":[220],"desired":[221],"cost":[225],"paid":[228],"increased":[233],"qubit":[235],"overhead":[236],"number":[239],"gates":[243],"grows.":[244],"To":[245],"illustrate":[246],"methodology,":[248],"construct":[250],"families":[253],"addressable":[257],"multi-controlled":[261]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-08-22T00:00:00"}
