{"id":"https://openalex.org/W7220668486","doi":"https://doi.org/10.48550/arxiv.2610.04621","title":"Exact Clifford Optimality for Two-Sided Locally Randomized Classical Shadows","display_name":"Exact Clifford Optimality for Two-Sided Locally Randomized Classical Shadows","publication_year":2026,"publication_date":"2026-10-03","ids":{"openalex":"https://openalex.org/W7220668486","doi":"https://doi.org/10.48550/arxiv.2610.04621"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04621","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04621","pdf_url":"https://arxiv.org/pdf/2610.04621","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/2610.04621","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023190892","display_name":"Xiaotian Nie","orcid":"https://orcid.org/0000-0002-1348-373X","observed_orcids":["https://orcid.org/0000-0002-1348-373X"]},"institutions":[{"id":"https://openalex.org/I4401726934","display_name":"IFlyTek (China)","ror":"https://ror.org/009pwww24","country_code":"CN","type":"company","lineage":["https://openalex.org/I4401726934"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nie, Xiaotian","raw_affiliation_strings":["Intelligent Quantum Inception Co., Ltd. , Haidian , Beijing , 100083 , China","iFLYTEK Research , Hefei , 230088 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intelligent Quantum Inception Co., Ltd. , Haidian , Beijing , 100083 , China","institution_ids":[]},{"raw_affiliation_string":"iFLYTEK Research , Hefei , 230088 , China","institution_ids":["https://openalex.org/I4401726934"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157756202","display_name":"Tao Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Tao","raw_affiliation_strings":["Institute for Advanced Study , Tsinghua University , Beijing 100084 , China","Intelligent Quantum Inception Co., Ltd. , Haidian , Beijing , 100083 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study , Tsinghua University , Beijing 100084 , China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Intelligent Quantum Inception Co., Ltd. , Haidian , Beijing , 100083 , China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5141275657","display_name":"Yadong Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wu, Yadong","raw_affiliation_strings":["College of Physics , Sichuan University , Chengdu 610065 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Physics , Sichuan University , Chengdu 610065 , China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5133548259","display_name":"Linghui Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4401726934","display_name":"IFlyTek (China)","ror":"https://ror.org/009pwww24","country_code":"CN","type":"company","lineage":["https://openalex.org/I4401726934"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Linghui","raw_affiliation_strings":["Intelligent Quantum Inception Co., Ltd. , Haidian , Beijing , 100083 , China","iFLYTEK Research , Hefei , 230088 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intelligent Quantum Inception Co., Ltd. , Haidian , Beijing , 100083 , China","institution_ids":[]},{"raw_affiliation_string":"iFLYTEK Research , Hefei , 230088 , China","institution_ids":["https://openalex.org/I4401726934"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.9115999937057495,"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":0.9115999937057495,"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":0.07930000126361847,"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":0.004999999888241291,"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/classical-shadows","display_name":"classical shadows","score":0.9509999752044678},{"id":"https://openalex.org/keywords/pauli-strings","display_name":"Pauli strings","score":0.7300000190734863},{"id":"https://openalex.org/keywords/many-body-correlations","display_name":"many-body correlations","score":0.7059999704360962},{"id":"https://openalex.org/keywords/optimal-circuit-design","display_name":"optimal circuit design","score":0.4339999854564667},{"id":"https://openalex.org/keywords/quantum-state-tomography","display_name":"quantum state tomography","score":0.4350000023841858}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7318999767303467},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6901000142097473},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.6502000093460083},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.47920000553131104},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.420199990272522},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4180999994277954},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.4113999903202057},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.3982999920845032},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.3937000036239624},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36410000920295715},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3521000146865845},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.350600004196167},{"id":"https://openalex.org/C180347388","wikidata":"https://www.wikidata.org/wiki/Q336233","display_name":"Pauli matrices","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C32955637","wikidata":"https://www.wikidata.org/wiki/Q684363","display_name":"Special unitary group","level":2,"score":0.32120001316070557},{"id":"https://openalex.org/C117797892","wikidata":"https://www.wikidata.org/wiki/Q286363","display_name":"Shadow (psychology)","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C130295795","wikidata":"https://www.wikidata.org/wiki/Q3550684","display_name":"Unitarity","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29490000009536743},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.26570001244544983},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2590000033378601},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.2551000118255615},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04621","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04621","pdf_url":"https://arxiv.org/pdf/2610.04621","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.2610.04621","doi":"https://doi.org/10.48550/arxiv.2610.04621","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04621","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.04621","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04621","pdf_url":"https://arxiv.org/pdf/2610.04621","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220668486.pdf","grobid_xml":"https://content.openalex.org/works/W7220668486.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4405901463","https://openalex.org/W4415316654"],"related_works":["https://openalex.org/W7202227757","https://openalex.org/W4393044935","https://openalex.org/W4297940708","https://openalex.org/W4386734525","https://openalex.org/W4417210203","https://openalex.org/W4399302682","https://openalex.org/W4399740412","https://openalex.org/W4390660290","https://openalex.org/W2744675565","https://openalex.org/W7212182415"],"abstract_inverted_index":{"Entangling":[0],"measurements":[1],"can":[2],"reduce":[3],"the":[4,46,64,104,116,134],"cost":[5],"of":[6,28,107],"learning":[7],"many-body":[8],"correlations.":[9],"We":[10],"consider":[11],"classical":[12],"shadows":[13],"in":[14],"which":[15,35],"a":[16,20,53],"fixed":[17],"unitary":[18,37,112,136],"on":[19,45],"$k$-qubit":[21],"region":[22],"is":[23,74,113,131],"sandwiched":[24],"between":[25],"two":[26],"layers":[27],"random":[29],"single-qubit":[30],"Clifford":[31,71],"gates,":[32],"and":[33,82,115,140],"ask":[34],"middle":[36,72],"best":[38],"estimates":[39],"Pauli":[40],"strings":[41],"with":[42,52],"full":[43],"support":[44,50],"region.":[47],"Combining":[48],"symplectic":[49],"counting":[51],"constraint":[54],"from":[55,119],"operator-size":[56],"parity,":[57],"we":[58,141],"prove":[59],"that":[60,129,143],"within":[61],"this":[62,96,144],"architecture":[63],"minimum":[65,97],"squared":[66],"shadow":[67],"norm":[68],"over":[69,133],"all":[70],"unitaries":[73],"$C_k^{\\rm":[75,83,102],"opt}=4\\cdot":[76,84],"9^k/(3\\cdot":[77,85],"5^k+3^k-6)$":[78],"for":[79,87,98,146],"odd":[80],"$k$":[81],"5^k-3^k+2)$":[86],"even":[88],"$k$.":[89,100,148],"A":[90],"dual-axis":[91],"rotation":[92],"circuit":[93],"$U_*$":[94,130],"attains":[95],"every":[99,147],"Asymptotically":[101],"opt}\\simeq(4/3)\\cdot(9/5)^k$:":[103],"exponential":[105],"base":[106],"Wu":[108],"et":[109],"al.'s":[110],"contractive":[111],"optimal,":[114],"prefactor":[117],"improves":[118],"$2$":[120],"to":[121],"$4/3$.":[122],"For":[123],"$1\\leq":[124],"k\\leq7$,":[125],"exact":[126],"certificates":[127],"show":[128],"optimal":[132],"entire":[135],"group":[137],"$\\mathrm":[138],"U(2^k)$,":[139],"conjecture":[142],"holds":[145]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}