{"id":"https://openalex.org/W4414021351","doi":"https://doi.org/10.22331/q-2025-09-05-1848","title":"A Theory of Direct Randomized Benchmarking","display_name":"A Theory of Direct Randomized Benchmarking","publication_year":2025,"publication_date":"2025-09-05","ids":{"openalex":"https://openalex.org/W4414021351","doi":"https://doi.org/10.22331/q-2025-09-05-1848"},"language":"en","primary_location":{"id":"doi:10.22331/q-2025-09-05-1848","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-09-05-1848","pdf_url":"https://quantum-journal.org/papers/q-2025-09-05-1848/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2025-09-05-1848/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042039348","display_name":"Anthony Polloreno","orcid":"https://orcid.org/0000-0003-1235-9531"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]},{"id":"https://openalex.org/I137473845","display_name":"Joint Institute for Laboratory Astrophysics","ror":"https://ror.org/008hybe55","country_code":"US","type":"facility","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065","https://openalex.org/I137473845","https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anthony M. Polloreno","raw_affiliation_strings":["JILA, NIST and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309, USA","Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"JILA, NIST and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309, USA","institution_ids":["https://openalex.org/I137473845"]},{"raw_affiliation_string":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185","institution_ids":["https://openalex.org/I192454743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085393475","display_name":"Arnaud Carignan-Dugas","orcid":"https://orcid.org/0000-0002-2036-2688"},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Arnaud Carignan-Dugas","raw_affiliation_strings":["Institute for Quantum Computing and the Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada","Keysight Technologies Canada, Kanata, ON K2K 2W5, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing and the Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Keysight Technologies Canada, Kanata, ON K2K 2W5, Canada","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038612688","display_name":"Jordan Hines","orcid":"https://orcid.org/0000-0001-5126-7256"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jordan Hines","raw_affiliation_strings":["Department of Physics, University of California, Berkeley, CA 94720","Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of California, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185","institution_ids":["https://openalex.org/I192454743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032976159","display_name":"Robin Blume-Kohout","orcid":"https://orcid.org/0000-0001-8134-948X"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robin Blume-Kohout","raw_affiliation_strings":["Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185","institution_ids":["https://openalex.org/I192454743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011333791","display_name":"Kevin Young","orcid":"https://orcid.org/0000-0002-4679-4542"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kevin Young","raw_affiliation_strings":["Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185","institution_ids":["https://openalex.org/I192454743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089944153","display_name":"Timothy Proctor","orcid":"https://orcid.org/0000-0003-0219-8930"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timothy Proctor","raw_affiliation_strings":["Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185","institution_ids":["https://openalex.org/I192454743"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5042039348"],"corresponding_institution_ids":["https://openalex.org/I137473845","https://openalex.org/I192454743"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":6.2328,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.96298978,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"9","issue":null,"first_page":"1848","last_page":"1848"},"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":0.9995999932289124,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9994999766349792,"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/benchmarking","display_name":"Benchmarking","score":0.8629440069198608},{"id":"https://openalex.org/keywords/randomized-controlled-trial","display_name":"Randomized controlled trial","score":0.4359641373157501},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3615122437477112},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.19285637140274048},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.16017839312553406},{"id":"https://openalex.org/keywords/internal-medicine","display_name":"Internal medicine","score":0.09470313787460327},{"id":"https://openalex.org/keywords/marketing","display_name":"Marketing","score":0.05205130577087402}],"concepts":[{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.8629440069198608},{"id":"https://openalex.org/C168563851","wikidata":"https://www.wikidata.org/wiki/Q1436668","display_name":"Randomized controlled trial","level":2,"score":0.4359641373157501},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3615122437477112},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.19285637140274048},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.16017839312553406},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.09470313787460327},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.05205130577087402}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2025-09-05-1848","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-09-05-1848","pdf_url":"https://quantum-journal.org/papers/q-2025-09-05-1848/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:57fb040b077c48a7a686cacdb6ab30cc","is_oa":true,"landing_page_url":"https://doaj.org/article/57fb040b077c48a7a686cacdb6ab30cc","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 9, p 1848 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2025-09-05-1848","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-09-05-1848","pdf_url":"https://quantum-journal.org/papers/q-2025-09-05-1848/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320312530","display_name":"Office of the Director of National Intelligence","ror":"https://ror.org/01v3fsc55"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414021351.pdf","grobid_xml":"https://content.openalex.org/works/W4414021351.grobid-xml"},"referenced_works_count":107,"referenced_works":["https://openalex.org/W1520080511","https://openalex.org/W1532834996","https://openalex.org/W1533625736","https://openalex.org/W1551139065","https://openalex.org/W1567452835","https://openalex.org/W1848366941","https://openalex.org/W1895592099","https://openalex.org/W1965985358","https://openalex.org/W1968850365","https://openalex.org/W1974169933","https://openalex.org/W1991022685","https://openalex.org/W2011109561","https://openalex.org/W2017477211","https://openalex.org/W2019630194","https://openalex.org/W2030467629","https://openalex.org/W2032147770","https://openalex.org/W2035496193","https://openalex.org/W2047639422","https://openalex.org/W2051017200","https://openalex.org/W2052146120","https://openalex.org/W2054324003","https://openalex.org/W2062506119","https://openalex.org/W2068704276","https://openalex.org/W2077595226","https://openalex.org/W2079099822","https://openalex.org/W2088468720","https://openalex.org/W2090368878","https://openalex.org/W2092458348","https://openalex.org/W2122082290","https://openalex.org/W2125457426","https://openalex.org/W2140622323","https://openalex.org/W2144105074","https://openalex.org/W2148118219","https://openalex.org/W2170620327","https://openalex.org/W2211717363","https://openalex.org/W2263382461","https://openalex.org/W2268604949","https://openalex.org/W2290336547","https://openalex.org/W2296095078","https://openalex.org/W2338653245","https://openalex.org/W2437693805","https://openalex.org/W2471819066","https://openalex.org/W2482126025","https://openalex.org/W2496565497","https://openalex.org/W2583795980","https://openalex.org/W2593843216","https://openalex.org/W2601605887","https://openalex.org/W2604172699","https://openalex.org/W2613136543","https://openalex.org/W2619816662","https://openalex.org/W2620407091","https://openalex.org/W2626992219","https://openalex.org/W2745278755","https://openalex.org/W2746656048","https://openalex.org/W2774683389","https://openalex.org/W2776564547","https://openalex.org/W2784023939","https://openalex.org/W2784264055","https://openalex.org/W2792514889","https://openalex.org/W2794135343","https://openalex.org/W2884175209","https://openalex.org/W2888421625","https://openalex.org/W2898615021","https://openalex.org/W2904416995","https://openalex.org/W2907653880","https://openalex.org/W2945916077","https://openalex.org/W2949178668","https://openalex.org/W2952602994","https://openalex.org/W2964120760","https://openalex.org/W2969837183","https://openalex.org/W2982169647","https://openalex.org/W3008681071","https://openalex.org/W3012928806","https://openalex.org/W3037318174","https://openalex.org/W3043678617","https://openalex.org/W3088995371","https://openalex.org/W3093093080","https://openalex.org/W3093975518","https://openalex.org/W3097248269","https://openalex.org/W3098892212","https://openalex.org/W3099175659","https://openalex.org/W3099956201","https://openalex.org/W3100111077","https://openalex.org/W3100462875","https://openalex.org/W3100641964","https://openalex.org/W3100755341","https://openalex.org/W3102622152","https://openalex.org/W3102805933","https://openalex.org/W3103203353","https://openalex.org/W3104213228","https://openalex.org/W3105872076","https://openalex.org/W3110543860","https://openalex.org/W3122989613","https://openalex.org/W3123208069","https://openalex.org/W3134135007","https://openalex.org/W3135729117","https://openalex.org/W3211481639","https://openalex.org/W3213277701","https://openalex.org/W3216902878","https://openalex.org/W4206310632","https://openalex.org/W4240454080","https://openalex.org/W4251600720","https://openalex.org/W4252740254","https://openalex.org/W4303184080","https://openalex.org/W4379466288","https://openalex.org/W4388668271","https://openalex.org/W4401611924"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4238897586","https://openalex.org/W435179959","https://openalex.org/W2619091065","https://openalex.org/W2059640416","https://openalex.org/W1490753184","https://openalex.org/W2284465472","https://openalex.org/W2291782699"],"abstract_inverted_index":{"Randomized":[0],"benchmarking":[1,124],"(RB)":[2],"protocols":[3],"are":[4],"widely":[5],"used":[6,83],"to":[7,56,84,99,141,147,177,209,252],"measure":[8],"an":[9,100,107],"average":[10,211],"error":[11,87,96,101,170],"rate":[12,88,206],"for":[13,158,184,229,241,255,261],"a":[14,32,64,113,125,131,138,199],"set":[15],"of":[16,24,63,89,119,163,169,213,267,288],"quantum":[17],"logic":[18],"gates.":[19,45,134],"However,":[20],"the":[21,57,61,86,167,194,204,210,214,286],"standard":[22,79,94,120,256],"version":[23],"RB":[25,80,111,150,181,196,238,263,277],"is":[26,81,106,112,182,198,207,226,239],"limited":[27],"because":[28,60],"it":[29,55],"only":[30],"benchmarks":[31],"processor's":[33,132],"native":[34,90,103,133],"gates":[35,53,185,242],"indirectly,":[36],"by":[37,92,122],"using":[38,249],"them":[39],"in":[40,174],"composite":[41,66],"<mml:math":[42,50,67,75],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>n</mml:mi></mml:math>-qubit":[43,51,68],"Clifford":[44,52,69,98],"Standard":[46],"RB's":[47,95],"reliance":[48],"on":[49,274,285],"restricts":[54],"few-qubit":[58],"regime,":[59],"fidelity":[62],"typical":[65],"gate":[70,127],"decreases":[71],"rapidly":[72],"with":[73],"increasing":[74],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>n</mml:mi></mml:math>.":[76],"Furthermore,":[77],"although":[78],"often":[82],"infer":[85],"gates,":[91,216],"rescaling":[93],"per":[97,102],"gate,":[104],"this":[105],"unreliable":[108],"extrapolation.":[109],"Direct":[110],"method":[114],"that":[115,179,186,193,203,223,236,243],"addresses":[116],"these":[117,164,280],"limitations":[118],"RB,":[121,143],"directly":[123],"customizable":[126],"set,":[128],"such":[129],"as":[130],"Here":[135],"we":[136,144,153],"provide":[137,271,282],"detailed":[139],"introduction":[140],"direct":[142,149,159,180,195,237,262,276,289],"discuss":[145],"how":[146],"design":[148],"experiments,":[151],"and":[152,202,269],"present":[154],"two":[155,259],"complementary":[156,265,272],"theories":[157,165,254,260,281],"RB.":[160,231,257,290],"The":[161],"first":[162],"uses":[166],"concept":[168],"propagation":[171],"or":[172],"scrambling":[173],"random":[175],"circuits":[176],"show":[178],"reliable":[183,230,240],"experience":[187,244],"stochastic":[188],"Pauli":[189],"errors.":[190],"We":[191],"prove":[192],"decay":[197,205],"single":[200],"exponential,":[201],"equal":[208],"infidelity":[212],"benchmarked":[215],"under":[217],"broad":[218],"circumstances.":[219],"This":[220],"theory":[221,234],"shows":[222],"group":[224],"twirling":[225],"not":[227],"required":[228],"Our":[232,258],"second":[233],"proves":[235],"general":[245],"gate-dependent":[246],"Markovian":[247],"errors,":[248],"similar":[250],"techniques":[251],"contemporary":[253],"have":[264],"regimes":[266],"applicability,":[268],"they":[270],"perspectives":[273],"why":[275],"works.":[278],"Together":[279],"comprehensive":[283],"guarantees":[284],"reliability":[287]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}