{"id":"https://openalex.org/W7128495131","doi":"https://doi.org/10.22331/q-2026-02-10-2003","title":"Theory of quantum error mitigation for non-Clifford gates","display_name":"Theory of quantum error mitigation for non-Clifford gates","publication_year":2026,"publication_date":"2026-02-10","ids":{"openalex":"https://openalex.org/W7128495131","doi":"https://doi.org/10.22331/q-2026-02-10-2003"},"language":"en","primary_location":{"id":"doi:10.22331/q-2026-02-10-2003","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-02-10-2003","pdf_url":null,"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://doi.org/10.22331/q-2026-02-10-2003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025428128","display_name":"David Layden","orcid":"https://orcid.org/0000-0002-1292-9007"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David Layden","raw_affiliation_strings":["IBM Research"],"affiliations":[{"raw_affiliation_string":"IBM Research","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125531121","display_name":"Bradley Mitchell","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bradley Mitchell","raw_affiliation_strings":["IBM Research"],"affiliations":[{"raw_affiliation_string":"IBM Research","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125493779","display_name":"Karthik Siva","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karthik Siva","raw_affiliation_strings":["IBM Research"],"affiliations":[{"raw_affiliation_string":"IBM Research","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025428128"],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.93133181,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":null,"first_page":"2003","last_page":"2003"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.8389999866485596,"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":0.8389999866485596,"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":0.1062999963760376,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.018300000578165054,"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/quantum-gate","display_name":"Quantum gate","score":0.7164999842643738},{"id":"https://openalex.org/keywords/controlled-not-gate","display_name":"Controlled NOT gate","score":0.6352999806404114},{"id":"https://openalex.org/keywords/quantum-circuit","display_name":"Quantum circuit","score":0.620199978351593},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.5968999862670898},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.49559998512268066},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4772000014781952},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.45829999446868896},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4447000026702881},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.42160001397132874},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.39309999346733093}],"concepts":[{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.7164999842643738},{"id":"https://openalex.org/C182953411","wikidata":"https://www.wikidata.org/wiki/Q917713","display_name":"Controlled NOT gate","level":5,"score":0.6352999806404114},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.620199978351593},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.5968999862670898},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5271000266075134},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.49559998512268066},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4772000014781952},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.45829999446868896},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4447000026702881},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4262999892234802},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.42160001397132874},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.3817000091075897},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.3517000079154968},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3255999982357025},{"id":"https://openalex.org/C111996192","wikidata":"https://www.wikidata.org/wiki/Q7269075","display_name":"Quantum noise","level":3,"score":0.3140000104904175},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31349998712539673},{"id":"https://openalex.org/C180347388","wikidata":"https://www.wikidata.org/wiki/Q336233","display_name":"Pauli matrices","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C201866948","wikidata":"https://www.wikidata.org/wiki/Q228206","display_name":"Random number generation","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C190463098","wikidata":"https://www.wikidata.org/wiki/Q2081419","display_name":"Quantum technology","level":4,"score":0.27090001106262207},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.2694000005722046},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.26919999718666077},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.26269999146461487},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.26260000467300415},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.25760000944137573},{"id":"https://openalex.org/C89143813","wikidata":"https://www.wikidata.org/wiki/Q17105423","display_name":"Quantum sensor","level":5,"score":0.25609999895095825},{"id":"https://openalex.org/C10418432","wikidata":"https://www.wikidata.org/wiki/Q560370","display_name":"AND gate","level":3,"score":0.2540000081062317},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2026-02-10-2003","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-02-10-2003","pdf_url":null,"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:6fac8b3be72344c9b30d4d149c4d2ab1","is_oa":true,"landing_page_url":"https://doaj.org/article/6fac8b3be72344c9b30d4d149c4d2ab1","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 10, p 2003 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2026-02-10-2003","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-02-10-2003","pdf_url":null,"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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1848366941","https://openalex.org/W1895592099","https://openalex.org/W1969341387","https://openalex.org/W1974169933","https://openalex.org/W2015711858","https://openalex.org/W2019630194","https://openalex.org/W2030467629","https://openalex.org/W2040792108","https://openalex.org/W2197609911","https://openalex.org/W2268604949","https://openalex.org/W2471819066","https://openalex.org/W2558921197","https://openalex.org/W2562526363","https://openalex.org/W2775106578","https://openalex.org/W2778498694","https://openalex.org/W2901677314","https://openalex.org/W2935584343","https://openalex.org/W2945916077","https://openalex.org/W2950805899","https://openalex.org/W2952602994","https://openalex.org/W2966125890","https://openalex.org/W2995050112","https://openalex.org/W3011002537","https://openalex.org/W3037303154","https://openalex.org/W3043431549","https://openalex.org/W3112338261","https://openalex.org/W3115118081","https://openalex.org/W3194228500","https://openalex.org/W3208514896","https://openalex.org/W4307283983","https://openalex.org/W4313494717","https://openalex.org/W4375859090","https://openalex.org/W4380627387","https://openalex.org/W4387542025","https://openalex.org/W4389672456","https://openalex.org/W4389892080","https://openalex.org/W4393220741","https://openalex.org/W4395661183","https://openalex.org/W4402331960","https://openalex.org/W4403333093","https://openalex.org/W4404849654","https://openalex.org/W4405923571","https://openalex.org/W4408023888"],"related_works":[],"abstract_inverted_index":{"Quantum":[0],"error":[1,105,111,255,286],"mitigation":[2,106],"techniques":[3,24,107,126,195,219],"mimic":[4],"noiseless":[5],"quantum":[6,87,145],"circuits":[7,13,83],"by":[8,159],"running":[9],"several":[10],"related":[11,116,241,268],"noisy":[12,33,69,200,266],"and":[14,76,78,95,114,130,164,225,229,232,245,281],"combining":[15],"their":[16,270],"outputs":[17],"in":[18,82,178,188,285],"particular":[19],"ways.":[20],"How":[21],"well":[22],"such":[23,90,186],"work":[25],"is":[26,272],"thought":[27],"to":[28,85,108,127,140,172,196,222,242,279,296],"depend":[29],"strongly":[30],"on":[31],"how":[32,139],"the":[34,102,115,153,166,252],"underlying":[35],"gates":[36,92,163,187,262],"are.":[37],"Weakly-entangling":[38],"gates,":[39,73,129,180],"like":[40,74],"<mml:math":[41,60,201],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[42,61,202],"<mml:msub>":[43,203],"<mml:mi>R</mml:mi>":[44,204],"<mml:mrow":[45,205],"class=\"MJX-TeXAtom-ORD\">":[46,206],"<mml:mi>Z</mml:mi>":[47,48,207,208],"</mml:mrow>":[49,209],"</mml:msub>":[50,210],"<mml:mo":[51,54,211,214],"stretchy=\"false\">(</mml:mo>":[52,212],"<mml:mi>&amp;#x03B8;</mml:mi>":[53,62,213],"stretchy=\"false\">)</mml:mo>":[55,215],"</mml:math>":[56,63,216],"for":[57,199,236],"small":[58],"angles":[59],",":[64],"can":[65,183,263,277,291],"be":[66,248,264,292,297],"much":[67],"less":[68,265],"than":[70,267],"entangling":[71],"Clifford":[72],"CNOT":[75],"CZ,":[77],"they":[79],"arise":[80],"naturally":[81],"used":[84],"simulate":[86],"dynamics.":[88],"However,":[89],"weakly-entangling":[91],"are":[93,96,220,240],"non-Clifford,":[94],"therefore":[97,193],"incompatible":[98],"with":[99],"two":[100,132],"of":[101,118,155,249,254],"most":[103],"prominent":[104],"date:":[109],"probabilistic":[110],"cancellation":[112],"(PEC)":[113],"form":[117],"zero-noise":[119],"extrapolation":[120],"(ZNE).":[121],"This":[122,169],"paper":[123],"generalizes":[124],"these":[125],"non-Clifford":[128,179,261],"comprises":[131],"complementary":[133],"parts.":[134],"The":[135,190],"first":[136,184],"part":[137,192],"shows":[138],"effectively":[141],"transform":[142],"any":[143,149],"given":[144],"channel":[146],"into":[147],"(almost)":[148],"desired":[150],"channel,":[151],"at":[152],"cost":[154],"a":[156],"sampling":[157],"overhead,":[158],"adding":[160],"random":[161],"Pauli":[162],"processing":[165],"measurement":[167,226],"outcomes.":[168],"enables":[170],"us":[171],"cancel":[173],"or":[174],"properly":[175],"amplify":[176],"noise":[177,271],"provided":[181],"we":[182],"characterize":[185],"detail.":[189],"second":[191],"introduces":[194],"do":[197],"so":[198],"gates.":[217],"These":[218],"robust":[221],"state":[223],"preparation":[224],"(SPAM)":[227],"errors,":[228],"exhibit":[230],"concentration":[231],"sensitivity\u2014crucial":[233],"statistical":[234],"properties":[235],"many":[237],"experiments.":[238],"They":[239],"randomized":[243],"benchmarking,":[244],"may":[246],"also":[247],"interest":[250],"beyond":[251],"context":[253],"mitigation.":[256,287],"We":[257],"find":[258],"that":[259],"while":[260],"Cliffords,":[269],"fundamentally":[273],"more":[274],"complex,":[275],"which":[276],"lead":[278],"surprising":[280],"sometimes":[282],"unwanted":[283],"effects":[284],"Whether":[288],"this":[289],"trade-off":[290],"broadly":[293],"advantageous":[294],"remains":[295],"seen.":[298]},"counts_by_year":[],"updated_date":"2026-02-12T08:01:53.621143","created_date":"2026-02-11T00:00:00"}