{"id":"https://openalex.org/W7221977109","doi":"https://doi.org/10.48550/arxiv.2610.20515","title":"Petz Recovery through a Single Polar Transformation for Approximate Quantum Error Correction","display_name":"Petz Recovery through a Single Polar Transformation for Approximate Quantum Error Correction","publication_year":2026,"publication_date":"2026-10-14","ids":{"openalex":"https://openalex.org/W7221977109","doi":"https://doi.org/10.48550/arxiv.2610.20515"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.20515","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20515","pdf_url":"https://arxiv.org/pdf/2610.20515","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/2610.20515","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158831629","display_name":"Hanzhang Zhao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhao, Hanzhang","raw_affiliation_strings":["Department of Physics & Astronomy , Texas A&M University , College Station , Texas 77843 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics & Astronomy , Texas A&M University , College Station , Texas 77843 , USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025529150","display_name":"Shenglong Xu","orcid":"https://orcid.org/0000-0002-8591-5562","observed_orcids":["https://orcid.org/0000-0002-8591-5562"]},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xu, Shenglong","raw_affiliation_strings":["Department of Physics & Astronomy , Texas A&M University , College Station , Texas 77843 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics & Astronomy , Texas A&M University , College Station , Texas 77843 , USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I91045830"],"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":0.9984999895095825,"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":0.9984999895095825,"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":0.0008999999845400453,"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/T11804","display_name":"Quantum many-body systems","score":0.00019999999494757503,"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/petz-recovery-map","display_name":"Petz recovery map","score":0.9190000295639038},{"id":"https://openalex.org/keywords/approximate-quantum-error-correction","display_name":"approximate quantum error correction","score":0.9819999933242798},{"id":"https://openalex.org/keywords/quantum-singular-value-transformation","display_name":"quantum singular value transformation","score":0.9810000061988831},{"id":"https://openalex.org/keywords/polynomial-approximation","display_name":"polynomial approximation","score":0.6039999723434448},{"id":"https://openalex.org/keywords/circuit-depth","display_name":"circuit depth","score":0.5659999847412109}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8094000220298767},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.4821000099182129},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4603999853134155},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4442000091075897},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4311000108718872},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.42660000920295715},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.40389999747276306},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.3935000002384186},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.3427000045776367},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.34130001068115234},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C137627569","wikidata":"https://www.wikidata.org/wiki/Q245471","display_name":"Cyclic redundancy check","level":3,"score":0.33090001344680786},{"id":"https://openalex.org/C182548165","wikidata":"https://www.wikidata.org/wiki/Q2261483","display_name":"Scrambling","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3260999917984009},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3215999901294708},{"id":"https://openalex.org/C136695289","wikidata":"https://www.wikidata.org/wiki/Q415568","display_name":"Bitstream","level":3,"score":0.301800012588501},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.2980000078678131},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.262800008058548},{"id":"https://openalex.org/C40969351","wikidata":"https://www.wikidata.org/wiki/Q3516228","display_name":"Word error rate","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26030001044273376},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.25279998779296875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.20515","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20515","pdf_url":"https://arxiv.org/pdf/2610.20515","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.2610.20515","doi":"https://doi.org/10.48550/arxiv.2610.20515","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.20515","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:2610.20515","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20515","pdf_url":"https://arxiv.org/pdf/2610.20515","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":[{"id":"https://openalex.org/G7490854944","display_name":"CAREER: Explore Quantum Many-Body Dynamics Beyond Thermalization","funder_award_id":"2443462","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/F4320337367","display_name":"Division of Materials Research","ror":"https://ror.org/01pc7k308"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221977109.pdf","grobid_xml":"https://content.openalex.org/works/W7221977109.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1501376697","https://openalex.org/W1686679909","https://openalex.org/W2000470073","https://openalex.org/W2017150476","https://openalex.org/W2021115151","https://openalex.org/W2030467629","https://openalex.org/W2068143801","https://openalex.org/W2137591724","https://openalex.org/W2162644822","https://openalex.org/W2415656260","https://openalex.org/W2563989350","https://openalex.org/W2591783339","https://openalex.org/W2608364249","https://openalex.org/W2762636446","https://openalex.org/W2886418553","https://openalex.org/W2929692894","https://openalex.org/W2985502600","https://openalex.org/W3009271807","https://openalex.org/W3128655640","https://openalex.org/W4206000311","https://openalex.org/W4293227947","https://openalex.org/W4322491967","https://openalex.org/W4388093033","https://openalex.org/W4391100672","https://openalex.org/W4392155549","https://openalex.org/W4396881614","https://openalex.org/W4403714964","https://openalex.org/W4406931418","https://openalex.org/W4407308495","https://openalex.org/W4407841517","https://openalex.org/W4412631407","https://openalex.org/W4415280717","https://openalex.org/W4415318129","https://openalex.org/W4415910831","https://openalex.org/W4416866665","https://openalex.org/W4417223570","https://openalex.org/W7080137269","https://openalex.org/W7128052780","https://openalex.org/W7129306837","https://openalex.org/W7164353429","https://openalex.org/W7204954480","https://openalex.org/W7213206026"],"related_works":["https://openalex.org/W3194259926","https://openalex.org/W2591783339","https://openalex.org/W2947649513","https://openalex.org/W4403714964","https://openalex.org/W7204954480","https://openalex.org/W4415280717","https://openalex.org/W7171717263","https://openalex.org/W4412631407","https://openalex.org/W1999966329","https://openalex.org/W3039791778"],"abstract_inverted_index":{"The":[0],"Petz":[1,29,56,70,143],"recovery":[2,30,34,51,57,133,144],"map":[3],"provides":[4,80],"a":[5,36,76,81,108,141],"near":[6],"optimal":[7],"decoder":[8],"for":[9,85],"approximate":[10,55,67],"quantum":[11,38],"error":[12,96],"correction,":[13],"but":[14],"its":[15],"inverse":[16],"square-root":[17],"normalization":[18],"complicates":[19],"circuit":[20,130],"implementation.":[21],"We":[22,43,60],"use":[23],"the":[24,28,62,66,87,102,112,123,127],"polar":[25],"structure":[26],"of":[27,75,104],"isometry":[31,52],"to":[32,119],"implement":[33],"through":[35],"single":[37],"singular":[39,116],"value":[40],"transformation":[41],"(QSVT).":[42],"give":[44],"explicit":[45],"block-encoding":[46],"circuits":[47],"and":[48,68,122,132,135],"an":[49,94],"extended":[50],"that":[53,98],"yields":[54,93],"without":[58],"postselection.":[59],"bound":[61,97],"diamond":[63],"distance":[64],"between":[65,129],"ideal":[69],"encoding-recovery":[71],"channels":[72],"in":[73],"terms":[74],"spectrum-weighted":[77],"loss,":[78],"which":[79],"channel":[82],"specific":[83],"objective":[84],"optimizing":[86],"QSVT":[88,105],"angles.":[89],"Uniform":[90],"polynomial":[91],"approximation":[92],"asymptotic":[95],"decays":[99],"exponentially":[100],"with":[101],"number":[103],"iterations,":[106],"at":[107],"rate":[109],"controlled":[110],"by":[111],"smallest":[113],"nonzero":[114],"scaled":[115],"value.":[117],"Applications":[118],"Haar-random":[120],"encoding":[121],"Hayden-Preskill":[124],"protocol":[125],"illustrate":[126],"tradeoff":[128],"depth":[131],"accuracy":[134],"place":[136],"existing":[137],"scrambling":[138],"decoders":[139],"within":[140],"common":[142],"framework.":[145]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-16T00:00:00"}
