{"id":"https://openalex.org/W2796735861","doi":"https://doi.org/10.22331/q-2021-11-16-581","title":"Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors","display_name":"Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors","publication_year":2021,"publication_date":"2021-11-16","ids":{"openalex":"https://openalex.org/W2796735861","doi":"https://doi.org/10.22331/q-2021-11-16-581","mag":"2796735861"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-11-16-581","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-11-16-581","pdf_url":"https://quantum-journal.org/papers/q-2021-11-16-581/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":"preprint","indexed_in":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-11-16-581/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054712730","display_name":"Seth Merkel","orcid":null},"institutions":[{"id":"https://openalex.org/I200576644","display_name":"HRL Laboratories (United States)","ror":"https://ror.org/05p7te762","country_code":"US","type":"company","lineage":["https://openalex.org/I200576644"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Seth T. Merkel","raw_affiliation_strings":["HRL Laboratories, LLC 3011 Malibu Canyon Road, Malibu, CA 90265 USA","HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, CA 90265,#N#USA#N#"],"affiliations":[{"raw_affiliation_string":"HRL Laboratories, LLC 3011 Malibu Canyon Road, Malibu, CA 90265 USA","institution_ids":["https://openalex.org/I200576644"]},{"raw_affiliation_string":"HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, CA 90265,#N#USA#N#","institution_ids":["https://openalex.org/I200576644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069411274","display_name":"Emily Pritchett","orcid":null},"institutions":[{"id":"https://openalex.org/I200576644","display_name":"HRL Laboratories (United States)","ror":"https://ror.org/05p7te762","country_code":"US","type":"company","lineage":["https://openalex.org/I200576644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Emily J. Pritchett","raw_affiliation_strings":["HRL Laboratories, LLC 3011 Malibu Canyon Road, Malibu, CA 90265 USA","HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, CA 90265,#N#USA#N#"],"affiliations":[{"raw_affiliation_string":"HRL Laboratories, LLC 3011 Malibu Canyon Road, Malibu, CA 90265 USA","institution_ids":["https://openalex.org/I200576644"]},{"raw_affiliation_string":"HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, CA 90265,#N#USA#N#","institution_ids":["https://openalex.org/I200576644"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068393916","display_name":"Bryan H. Fong","orcid":"https://orcid.org/0009-0009-2881-2055"},"institutions":[{"id":"https://openalex.org/I200576644","display_name":"HRL Laboratories (United States)","ror":"https://ror.org/05p7te762","country_code":"US","type":"company","lineage":["https://openalex.org/I200576644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bryan H. Fong","raw_affiliation_strings":["HRL Laboratories, LLC 3011 Malibu Canyon Road, Malibu, CA 90265 USA","HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, CA 90265,#N#USA#N#"],"affiliations":[{"raw_affiliation_string":"HRL Laboratories, LLC 3011 Malibu Canyon Road, Malibu, CA 90265 USA","institution_ids":["https://openalex.org/I200576644"]},{"raw_affiliation_string":"HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, CA 90265,#N#USA#N#","institution_ids":["https://openalex.org/I200576644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054712730"],"corresponding_institution_ids":["https://openalex.org/I200576644"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.2592,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.83011888,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"5","issue":null,"first_page":"581","last_page":"581"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9983999729156494,"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":0.998199999332428,"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/benchmarking","display_name":"Benchmarking","score":0.5917640328407288},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4959753453731537},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49406149983406067},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44557759165763855},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.41672199964523315},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33851584792137146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29417023062705994},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19284763932228088}],"concepts":[{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.5917640328407288},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4959753453731537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49406149983406067},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44557759165763855},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.41672199964523315},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33851584792137146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29417023062705994},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19284763932228088},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.22331/q-2021-11-16-581","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-11-16-581","pdf_url":"https://quantum-journal.org/papers/q-2021-11-16-581/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":"mag:2796735861","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1804.05951.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:111010d3a3a147feb885c0a914a32398","is_oa":true,"landing_page_url":"https://doaj.org/article/111010d3a3a147feb885c0a914a32398","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 5, p 581 (2021)","raw_type":"article"},{"id":"doi:10.48550/arxiv.1804.05951","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.05951","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.22331/q-2021-11-16-581","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-11-16-581","pdf_url":"https://quantum-journal.org/papers/q-2021-11-16-581/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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2796735861.pdf","grobid_xml":"https://content.openalex.org/works/W2796735861.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1520080511","https://openalex.org/W1532834996","https://openalex.org/W1567452835","https://openalex.org/W1848366941","https://openalex.org/W1895592099","https://openalex.org/W1965985358","https://openalex.org/W1968850365","https://openalex.org/W1991022685","https://openalex.org/W1994099404","https://openalex.org/W2000443848","https://openalex.org/W2009654826","https://openalex.org/W2011109561","https://openalex.org/W2015590395","https://openalex.org/W2017477211","https://openalex.org/W2027127692","https://openalex.org/W2035496193","https://openalex.org/W2047639422","https://openalex.org/W2062506119","https://openalex.org/W2079099822","https://openalex.org/W2148118219","https://openalex.org/W2160877306","https://openalex.org/W2170620327","https://openalex.org/W2336871513","https://openalex.org/W2338653245","https://openalex.org/W2468792555","https://openalex.org/W2598789794","https://openalex.org/W2601605887","https://openalex.org/W2604172699","https://openalex.org/W2613136543","https://openalex.org/W2888421625","https://openalex.org/W2949178668","https://openalex.org/W2952914414","https://openalex.org/W2963562046","https://openalex.org/W3099332453","https://openalex.org/W3102094813","https://openalex.org/W3102429237","https://openalex.org/W3103203353","https://openalex.org/W3104213228"],"related_works":["https://openalex.org/W2170620327","https://openalex.org/W2148118219","https://openalex.org/W1965985358","https://openalex.org/W1848366941","https://openalex.org/W1532834996","https://openalex.org/W3103203353","https://openalex.org/W2017477211","https://openalex.org/W2601605887","https://openalex.org/W2338653245","https://openalex.org/W2079099822","https://openalex.org/W3104213228","https://openalex.org/W3099175659","https://openalex.org/W2784264055","https://openalex.org/W2770987847","https://openalex.org/W2897217696","https://openalex.org/W3160400124","https://openalex.org/W3168275631","https://openalex.org/W3179161035","https://openalex.org/W3212713369","https://openalex.org/W3098150664"],"abstract_inverted_index":{"We":[0,59],"show":[1,60],"that":[2,62,91],"the":[3,18,51,72,76,85,100,116,126,137,142],"Randomized":[4],"Benchmarking":[5],"(RB)":[6],"protocol":[7],"is":[8,69,82,120],"a":[9,89,112,121,133],"convolution":[10],"amenable":[11],"to":[12,71,97,103,110,141],"Fourier":[13,22],"space":[14],"analysis.":[15],"By":[16],"adopting":[17],"mathematical":[19],"framework":[20,106],"of":[21,24,43,53,75,88],"transforms":[23],"matrix-valued":[25],"functions":[26],"on":[27,50,56],"groups":[28],"established":[29],"in":[30,114],"recent":[31],"work":[32],"from":[33],"Gowers":[34],"and":[35,46,99],"Hatami":[36],"\\cite{GH15},":[37],"we":[38],"provide":[39],"an":[40,79],"alternative":[41],"proof":[42],"Wallman's":[44],"\\cite{Wallman2018}":[45],"Proctor's":[47],"\\cite{Proctor17}":[48],"bounds":[49],"effect":[52],"gate-dependent":[54],"noise":[55],"randomized":[57],"benchmarking.":[58],"explicitly":[61],"as":[63,65,130,132],"long":[64],"our":[66],"faulty":[67],"gate-set":[68,118],"close":[70,96,102],"targeted":[73],"representation":[74],"Clifford":[77],"group,":[78],"RB":[80,127],"sequence":[81],"described":[83],"by":[84,125],"exponential":[86],"decay":[87,128],"process":[90],"has":[92],"exactly":[93],"two":[94],"eigenvalues":[95],"one":[98],"rest":[101],"zero.":[104],"This":[105],"also":[107],"allows":[108],"us":[109],"construct":[111],"gauge":[113,134],"which":[115,135],"average":[117],"error":[119],"depolarizing":[122],"channel":[123],"parameterized":[124],"rates,":[129],"well":[131],"maximizes":[136],"fidelity":[138],"with":[139],"respect":[140],"ideal":[143],"gate-set.":[144]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}