{"id":"https://openalex.org/W2099641843","doi":"https://doi.org/10.1142/s0129054103002011","title":"EFFICIENT QUANTUM CIRCUITS FOR NON-QUBIT QUANTUM ERROR-CORRECTING CODES","display_name":"EFFICIENT QUANTUM CIRCUITS FOR NON-QUBIT QUANTUM ERROR-CORRECTING CODES","publication_year":2003,"publication_date":"2003-10-01","ids":{"openalex":"https://openalex.org/W2099641843","doi":"https://doi.org/10.1142/s0129054103002011","mag":"2099641843"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054103002011","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054103002011","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/quant-ph/0211014","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036635049","display_name":"Markus Grassl","orcid":"https://orcid.org/0000-0002-3720-5195"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I73544541","display_name":"Mathematical Sciences Research Institute","ror":"https://ror.org/05hs5r386","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I73544541"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"MARKUS GRASSL","raw_affiliation_strings":["Institut f\u00fcr Algorithmen und Kognitive Systeme, Universit\u00e4t Karlsruhe, Am Fasanengarten 5, 76 128 Karlsruhe, Germany","The Mathematical Sciences Research Institute, 1000 Centennial Drive, #5070, Berkeley, CA 94720-5070, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Algorithmen und Kognitive Systeme, Universit\u00e4t Karlsruhe, Am Fasanengarten 5, 76 128 Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"The Mathematical Sciences Research Institute, 1000 Centennial Drive, #5070, Berkeley, CA 94720-5070, USA","institution_ids":["https://openalex.org/I73544541"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109086831","display_name":"Martin R\u00f6tteler","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA","DE"],"is_corresponding":false,"raw_author_name":"MARTIN R\u00d6TTELER","raw_affiliation_strings":["Department of Combinatorics and Optimization,  Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada,  N2L 3G1, Canada","Institut f\u00fcr Algorithmen und Kognitive Systeme, Universit\u00e4t Karlsruhe, Am Fasanengarten 5, 76 128 Karlsruhe, Germany","Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization,  Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada,  N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Institut f\u00fcr Algorithmen und Kognitive Systeme, Universit\u00e4t Karlsruhe, Am Fasanengarten 5, 76 128 Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110013882","display_name":"Thomas Beth","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"THOMAS BETH","raw_affiliation_strings":["Institut f\u00fcr Algorithmen und Kognitive Systeme, Universit\u00e4t Karlsruhe, Am Fasanengarten 5, 76 128 Karlsruhe, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Algorithmen und Kognitive Systeme, Universit\u00e4t Karlsruhe, Am Fasanengarten 5, 76 128 Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.1136,"has_fulltext":false,"cited_by_count":107,"citation_normalized_percentile":{"value":0.96104972,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"05","first_page":"757","last_page":"775"},"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/T10020","display_name":"Quantum Information and Cryptography","score":0.996999979019165,"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":0.9912999868392944,"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/qubit","display_name":"Qubit","score":0.6520560383796692},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.5958940386772156},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4778729975223541},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4545005261898041},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.41325074434280396},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3690252900123596},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3456602990627289},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.327786386013031},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3263762593269348},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2705387473106384},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2680118680000305},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1022593080997467}],"concepts":[{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.6520560383796692},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.5958940386772156},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4778729975223541},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4545005261898041},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.41325074434280396},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3690252900123596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3456602990627289},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.327786386013031},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3263762593269348},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2705387473106384},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2680118680000305},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1022593080997467}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0129054103002011","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054103002011","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:quant-ph/0211014","is_oa":true,"landing_page_url":"http://arxiv.org/abs/quant-ph/0211014","pdf_url":"https://arxiv.org/pdf/quant-ph/0211014","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,"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":"pmh:oai:cds.cern.ch:590341","is_oa":false,"landing_page_url":"http://cds.cern.ch/record/590341","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:quant-ph/0211014","is_oa":true,"landing_page_url":"http://arxiv.org/abs/quant-ph/0211014","pdf_url":"https://arxiv.org/pdf/quant-ph/0211014","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,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W183777952","https://openalex.org/W1555219737","https://openalex.org/W1579786114","https://openalex.org/W1606480398","https://openalex.org/W1965075382","https://openalex.org/W1974293884","https://openalex.org/W1993813188","https://openalex.org/W2003177806","https://openalex.org/W2042474962","https://openalex.org/W2052169397","https://openalex.org/W2069711632","https://openalex.org/W2103713333","https://openalex.org/W2113797588","https://openalex.org/W2114207424","https://openalex.org/W2128751442","https://openalex.org/W2143438504","https://openalex.org/W2167413626","https://openalex.org/W2490728539","https://openalex.org/W2521284916","https://openalex.org/W2732251371","https://openalex.org/W2763302490","https://openalex.org/W2912120411","https://openalex.org/W2912318510","https://openalex.org/W3098556788","https://openalex.org/W3106206450","https://openalex.org/W4206278260","https://openalex.org/W4242597152","https://openalex.org/W4243157975","https://openalex.org/W4251109627"],"related_works":["https://openalex.org/W2010108838","https://openalex.org/W2949602549","https://openalex.org/W2761090343","https://openalex.org/W3033912009","https://openalex.org/W4212962264","https://openalex.org/W1982303606","https://openalex.org/W3177540191","https://openalex.org/W4388540582","https://openalex.org/W3126247638","https://openalex.org/W2143142748"],"abstract_inverted_index":{"We":[0],"present":[1],"two":[2],"methods":[3],"for":[4,10],"the":[5,43,56,61],"construction":[6],"of":[7,23,26,55],"quantum":[8,11,18,45,62],"circuits":[9],"error-":[12],"correcting":[13],"codes":[14],"(QECC).":[15],"The":[16,52],"underlying":[17],"systems":[19],"are":[20],"tensor":[21],"products":[22],"subsystems":[24],"(qudits)":[25],"equal":[27],"dimension":[28],"which":[29],"is":[30,64],"a":[31,35],"prime":[32],"power.":[33],"For":[34],"QECC":[36],"encoding":[37],"k":[38],"qudits":[39],"into":[40],"n":[41],"qudits,":[42],"resulting":[44],"circuit":[46,63],"has":[47],"O(n(n":[48,65],"-":[49,66],"k))":[50],"gates.":[51],"running":[53],"time":[54],"classical":[57],"algorithm":[58],"to":[59],"compute":[60],"k)":[67],"2":[68],").":[69]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
