{"id":"https://openalex.org/W7204269000","doi":"https://doi.org/10.1103/drwg-dgb7","title":"Error-Correction Transitions in Finite-Depth Quantum Channels","display_name":"Error-Correction Transitions in Finite-Depth Quantum Channels","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7204269000","doi":"https://doi.org/10.1103/drwg-dgb7","pmid":"https://pubmed.ncbi.nlm.nih.gov/42826961"},"language":"en","primary_location":{"id":"doi:10.1103/drwg-dgb7","doi":"https://doi.org/10.1103/drwg-dgb7","is_oa":false,"landing_page_url":"https://doi.org/10.1103/drwg-dgb7","pdf_url":null,"source":{"id":"https://openalex.org/S24807848","display_name":"Physical Review Letters","issn_l":"0031-9007","issn":["0031-9007","1079-7114","1092-0145"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Letters","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2603.20369","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148360970","display_name":"Anonymous","orcid":"https://orcid.org/0009-0004-4065-0320","observed_orcids":["https://orcid.org/0009-0004-4065-0320"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I187986737","display_name":"Coll\u00e8ge de France","ror":"https://ror.org/04ex24z53","country_code":"FR","type":"education","lineage":["https://openalex.org/I187986737"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I4210142324","display_name":"CY Cergy Paris Universit\u00e9","ror":"https://ror.org/043htjv09","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142324"]},{"id":"https://openalex.org/I4387153379","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","ror":"https://ror.org/05nhcdk38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210142324","https://openalex.org/I4387153379"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Arman Sauliere","raw_affiliation_strings":["CNRS","CY Cergy Paris Universit\u00e9","Coll\u00e8ge de France","Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","PSL Research University"],"raw_orcid":"https://orcid.org/0009-0004-4065-0320","affiliations":[{"raw_affiliation_string":"CNRS","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CY Cergy Paris Universit\u00e9","institution_ids":["https://openalex.org/I4210142324"]},{"raw_affiliation_string":"Coll\u00e8ge de France","institution_ids":["https://openalex.org/I187986737"]},{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","institution_ids":["https://openalex.org/I4387153379"]},{"raw_affiliation_string":"PSL Research University","institution_ids":["https://openalex.org/I2746051580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041684923","display_name":"Guglielmo Lami","orcid":"https://orcid.org/0000-0002-1778-7263","observed_orcids":["https://orcid.org/0000-0002-1778-7263"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I187986737","display_name":"Coll\u00e8ge de France","ror":"https://ror.org/04ex24z53","country_code":"FR","type":"education","lineage":["https://openalex.org/I187986737"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I4210142324","display_name":"CY Cergy Paris Universit\u00e9","ror":"https://ror.org/043htjv09","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142324"]},{"id":"https://openalex.org/I4387153379","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","ror":"https://ror.org/05nhcdk38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210142324","https://openalex.org/I4387153379"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Guglielmo Lami","raw_affiliation_strings":["CNRS","CY Cergy Paris Universit\u00e9","Coll\u00e8ge de France","Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","PSL Research University"],"raw_orcid":"https://orcid.org/0000-0002-1778-7263","affiliations":[{"raw_affiliation_string":"CNRS","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CY Cergy Paris Universit\u00e9","institution_ids":["https://openalex.org/I4210142324"]},{"raw_affiliation_string":"Coll\u00e8ge de France","institution_ids":["https://openalex.org/I187986737"]},{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","institution_ids":["https://openalex.org/I4387153379"]},{"raw_affiliation_string":"PSL Research University","institution_ids":["https://openalex.org/I2746051580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100665022","display_name":"Pedro Ribeiro","orcid":"https://orcid.org/0000-0001-7630-2054","observed_orcids":["https://orcid.org/0000-0001-7630-2054","https://orcid.org/0000-0001-8270-3663"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I4210142324","display_name":"CY Cergy Paris Universit\u00e9","ror":"https://ror.org/043htjv09","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142324"]},{"id":"https://openalex.org/I4387153379","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","ror":"https://ror.org/05nhcdk38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210142324","https://openalex.org/I4387153379"]}],"countries":["FR","PT"],"is_corresponding":false,"raw_author_name":"Pedro Ribeiro","raw_affiliation_strings":["CNRS","CY Cergy Paris Universit\u00e9","Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","Universidade de Lisboa"],"raw_orcid":"https://orcid.org/0000-0001-7630-2054","affiliations":[{"raw_affiliation_string":"CNRS","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CY Cergy Paris Universit\u00e9","institution_ids":["https://openalex.org/I4210142324"]},{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","institution_ids":["https://openalex.org/I4387153379"]},{"raw_affiliation_string":"Universidade de Lisboa","institution_ids":["https://openalex.org/I141596103"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011615977","display_name":"Andrea De Luca","orcid":"https://orcid.org/0000-0003-0272-5083","observed_orcids":["https://orcid.org/0000-0003-0272-5083"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210129651","display_name":"Laboratoire de Physique de l'Ecole Normale Sup\u00e9rieure","ror":"https://ror.org/03a26mh11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I2746051580","https://openalex.org/I2800004676","https://openalex.org/I29607241","https://openalex.org/I39804081","https://openalex.org/I4210129651"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Andrea De Luca","raw_affiliation_strings":["CNRS","ENS","Laboratoire de Physique de l\u2019\u00c9cole Normale Sup\u00e9rieure","Sorbonne Universit\u00e9","Universit\u00e9 PSL","Universit\u00e9 Paris-Cit\u00e9"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"ENS","institution_ids":["https://openalex.org/I29607241"]},{"raw_affiliation_string":"Laboratoire de Physique de l\u2019\u00c9cole Normale Sup\u00e9rieure","institution_ids":["https://openalex.org/I29607241","https://openalex.org/I4210129651"]},{"raw_affiliation_string":"Sorbonne Universit\u00e9","institution_ids":["https://openalex.org/I39804081"]},{"raw_affiliation_string":"Universit\u00e9 PSL","institution_ids":["https://openalex.org/I2746051580"]},{"raw_affiliation_string":"Universit\u00e9 Paris-Cit\u00e9","institution_ids":["https://openalex.org/I204730241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016712389","display_name":"Jacopo De Nardis","orcid":"https://orcid.org/0000-0001-7877-0329","observed_orcids":["https://orcid.org/0000-0001-7877-0329"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I187986737","display_name":"Coll\u00e8ge de France","ror":"https://ror.org/04ex24z53","country_code":"FR","type":"education","lineage":["https://openalex.org/I187986737"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I4210142324","display_name":"CY Cergy Paris Universit\u00e9","ror":"https://ror.org/043htjv09","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142324"]},{"id":"https://openalex.org/I4387153379","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","ror":"https://ror.org/05nhcdk38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210142324","https://openalex.org/I4387153379"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jacopo De Nardis","raw_affiliation_strings":["CNRS","CY Cergy Paris Universit\u00e9","Coll\u00e8ge de France","Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","PSL Research University"],"raw_orcid":"https://orcid.org/0000-0001-7877-0329","affiliations":[{"raw_affiliation_string":"CNRS","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CY Cergy Paris Universit\u00e9","institution_ids":["https://openalex.org/I4210142324"]},{"raw_affiliation_string":"Coll\u00e8ge de France","institution_ids":["https://openalex.org/I187986737"]},{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation","institution_ids":["https://openalex.org/I4387153379"]},{"raw_affiliation_string":"PSL Research University","institution_ids":["https://openalex.org/I2746051580"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":10,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3750,"currency":"USD","value_usd":3750},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.61472094,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"137","issue":"12","first_page":"120402","last_page":"120402"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.8672000169754028,"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":0.8672000169754028,"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/T11804","display_name":"Quantum many-body systems","score":0.06260000169277191,"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"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.0625,"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/quantum-error-correction","display_name":"quantum error correction","score":0.8019999861717224},{"id":"https://openalex.org/keywords/quantum-capacity","display_name":"quantum channel capacity","score":0.6909999847412109},{"id":"https://openalex.org/keywords/quantum-memory","display_name":"quantum memory","score":0.328000009059906}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7461000084877014},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.46790000796318054},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.44429999589920044},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.3666999936103821},{"id":"https://openalex.org/C72190298","wikidata":"https://www.wikidata.org/wiki/Q2118253","display_name":"Quantum phase transition","level":3,"score":0.2969000041484833},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.29249998927116394},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.2924000024795532},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C124657808","wikidata":"https://www.wikidata.org/wiki/Q1133068","display_name":"Quantum dot","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.2696000039577484},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.2583000063896179}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1103/drwg-dgb7","doi":"https://doi.org/10.1103/drwg-dgb7","is_oa":false,"landing_page_url":"https://doi.org/10.1103/drwg-dgb7","pdf_url":null,"source":{"id":"https://openalex.org/S24807848","display_name":"Physical Review Letters","issn_l":"0031-9007","issn":["0031-9007","1079-7114","1092-0145"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Letters","raw_type":"journal-article"},{"id":"pmid:42826961","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42826961","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review letters","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:2603.20369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2603.20369","pdf_url":"https://arxiv.org/pdf/2603.20369","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05769147v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-05769147","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Physical Review Letters, 2026, 137 (12), pp.120402. ⟨10.1103/drwg-dgb7⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2603.20369","doi":"https://doi.org/10.48550/arxiv.2603.20369","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.20369","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2603.20369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2603.20369","pdf_url":"https://arxiv.org/pdf/2603.20369","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1045576589","display_name":"Centro de F\u00edsica e Engenharia de Materiais Avan\u00e7ados","funder_award_id":"UID/04540/2025","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G1067308730","display_name":null,"funder_award_id":"101042293","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G2031922906","display_name":null,"funder_award_id":"UID /04540","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3398237449","display_name":null,"funder_award_id":"PHY-2309135","funder_id":"https://openalex.org/F4320337427","funder_display_name":"Kavli Institute for Theoretical Physics, University of California, Santa Barbara"},{"id":"https://openalex.org/G3796701426","display_name":null,"funder_award_id":"ANR-22-CPJ1-0021-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4360986921","display_name":null,"funder_award_id":"NSF PHY2309135","funder_id":"https://openalex.org/F4320337427","funder_display_name":"Kavli Institute for Theoretical Physics, University of California, Santa Barbara"},{"id":"https://openalex.org/G4689434848","display_name":null,"funder_award_id":"2309135","funder_id":"https://openalex.org/F4320337427","funder_display_name":"Kavli Institute for Theoretical Physics, University of California, Santa Barbara"},{"id":"https://openalex.org/G6997658380","display_name":null,"funder_award_id":"10.54499","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G7002119356","display_name":"Kavli Institute for Theoretical Physics","funder_award_id":"2309135","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"},{"id":"https://openalex.org/F4320337427","display_name":"Kavli Institute for Theoretical Physics, University of California, Santa Barbara","ror":"https://ror.org/02t274463"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204269000.pdf","grobid_xml":"https://content.openalex.org/works/W7204269000.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1409569118","https://openalex.org/W1643301482","https://openalex.org/W1826324575","https://openalex.org/W1969246646","https://openalex.org/W1975313455","https://openalex.org/W1977545330","https://openalex.org/W1999706070","https://openalex.org/W2001619599","https://openalex.org/W2002372750","https://openalex.org/W2021115151","https://openalex.org/W2033216491","https://openalex.org/W2040792108","https://openalex.org/W2070375169","https://openalex.org/W2087256203","https://openalex.org/W2129872856","https://openalex.org/W2154564336","https://openalex.org/W2179731956","https://openalex.org/W2290336547","https://openalex.org/W2512685237","https://openalex.org/W2594901681","https://openalex.org/W2620407091","https://openalex.org/W2781738013","https://openalex.org/W2804172638","https://openalex.org/W2945488351","https://openalex.org/W2949986970","https://openalex.org/W3008717942","https://openalex.org/W3023478445","https://openalex.org/W3043723517","https://openalex.org/W3107463944","https://openalex.org/W3135510046","https://openalex.org/W3200611022","https://openalex.org/W3203484453","https://openalex.org/W4288055134","https://openalex.org/W4293171638","https://openalex.org/W4386285077","https://openalex.org/W4386742491","https://openalex.org/W4389373471","https://openalex.org/W4389489960","https://openalex.org/W4390227513","https://openalex.org/W4393375706","https://openalex.org/W4406002251","https://openalex.org/W4408475821","https://openalex.org/W4410363868","https://openalex.org/W4410435348","https://openalex.org/W4414922368","https://openalex.org/W4414993016","https://openalex.org/W4415166328","https://openalex.org/W4415502950","https://openalex.org/W4416050326","https://openalex.org/W4416393130","https://openalex.org/W7118497389","https://openalex.org/W7204237199"],"related_works":["https://openalex.org/W4415318377","https://openalex.org/W7118497389","https://openalex.org/W1977545330","https://openalex.org/W4393375706","https://openalex.org/W3093986290","https://openalex.org/W2977694727","https://openalex.org/W4394856219","https://openalex.org/W2158050515","https://openalex.org/W2023101200","https://openalex.org/W1572877829"],"abstract_inverted_index":{"We":[0,25,76],"study":[1],"error-correction":[2],"protocols":[3],"in":[4,48,101,138],"which":[5,128],"a":[6,18,57,62,67,92],"quantum":[7],"channel":[8],"encodes":[9],"logical":[10],"information":[11,73],"into":[12],"an":[13],"enlarged":[14],"Hilbert":[15],"space":[16],"through":[17],"one-dimensional":[19],"random":[20],"circuit":[21,39,102,126],"with":[22],"local":[23],"gates.":[24],"consider":[26],"both":[27,49],"noise":[28,35,64,88],"acting":[29],"after":[30,91],"the":[31,37,42,51,79,111,115,120,125,130],"encoding":[32,38,98],"step":[33],"and":[34,133],"affecting":[36],"itself.":[40],"Using":[41],"coherent":[43],"information,":[44],"we":[45],"show":[46],"that":[47],"settings":[50],"infinite-depth":[52],"limit":[53],"is":[54,74,99,118,135],"governed":[55],"by":[56],"universal":[58,85],"random-matrix":[59],"transition":[60],"at":[61],"critical":[63],"rate,":[65],"separating":[66],"recoverable":[68],"phase":[69],"from":[70,83],"one":[71],"where":[72],"lost.":[75],"then":[77],"characterize":[78],"leading":[80],"finite-depth":[81],"deviations":[82],"this":[84],"regime.":[86],"When":[87,114],"acts":[89],"only":[90,136],"unitary":[93],"encoder,":[94],"convergence":[95,134],"to":[96],"perfect":[97],"exponential":[100],"depth,":[103],"although":[104],"boundary":[105],"effects":[106],"can":[107],"delay":[108],"saturation":[109],"beyond":[110],"design":[112],"time.":[113],"encoder":[116],"itself":[117],"noisy,":[119],"relevant":[121],"control":[122],"parameter":[123],"becomes":[124],"fidelity,":[127],"replaces":[129],"Hashing":[131],"bound,":[132],"polynomial":[137],"depth.":[139]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-08-27T00:00:00"}