{"id":"https://openalex.org/W7160388052","doi":"https://doi.org/10.48550/arxiv.2605.03685","title":"Quantum Multi-Level Estimation of Functionals of Discrete Distributions","display_name":"Quantum Multi-Level Estimation of Functionals of Discrete Distributions","publication_year":2026,"publication_date":"2026-05-05","ids":{"openalex":"https://openalex.org/W7160388052","doi":"https://doi.org/10.48550/arxiv.2605.03685"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.03685","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03685","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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.03685","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135479534","display_name":"Kean Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Kean","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112879987","display_name":"Minbo Gao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Minbo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135515768","display_name":"Tongyang Li","orcid":"https://orcid.org/0000-0002-1346-0677"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Tongyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135482182","display_name":"Qisheng Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Qisheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135489630","display_name":"Xinzhao Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Xinzhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.7141000032424927,"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":0.7141000032424927,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.04969999939203262,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.02810000069439411,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6919999718666077},{"id":"https://openalex.org/keywords/quantum-phase-estimation-algorithm","display_name":"Quantum phase estimation algorithm","score":0.5447999835014343},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5188000202178955},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5101000070571899},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.3935999870300293},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.35569998621940613},{"id":"https://openalex.org/keywords/quantum-operation","display_name":"Quantum operation","score":0.3476000130176544},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.3425999879837036},{"id":"https://openalex.org/keywords/quantum-capacity","display_name":"Quantum capacity","score":0.34209999442100525}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6919999718666077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6187000274658203},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.5447999835014343},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5188000202178955},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5101000070571899},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39430001378059387},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.3935999870300293},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.35569998621940613},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.3476000130176544},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34450000524520874},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.34209999442100525},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32519999146461487},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3199999928474426},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.30649998784065247},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.30410000681877136},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C95546049","wikidata":"https://www.wikidata.org/wiki/Q1345207","display_name":"Entropy estimation","level":3,"score":0.28360000252723694},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27880001068115234},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.25679999589920044},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.2540000081062317},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.2506999969482422},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.03685","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03685","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.03685","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03685","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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"score":0.5419753193855286,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"},{"score":0.43903395533561707,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,17],"propose":[1],"a":[2,8,13,94,129,137],"quantum":[3,77,96,130,138,166],"multi-level":[4],"estimation":[5,46],"framework":[6],"for":[7,79,168,171],"functional":[9],"$\\sum_{i=1}^n":[10],"f(p_i)$":[11],"of":[12,47,83],"discrete":[14,84],"distribution":[15],"$(p_i)_{i=1}^n$.":[16],"partition":[18],"the":[19,41,48,80,104,141,163],"values":[20],"$p_i$":[21],"into":[22],"logarithmically":[23],"many":[24],"intervals":[25],"whose":[26],"length":[27],"decays":[28],"exponentially.":[29],"For":[30,88,121],"each":[31],"interval,":[32],"we":[33,74,92,127],"perform":[34],"non-destructive":[35],"singular":[36],"value":[37],"discrimination":[38],"to":[39,109,146,160],"isolate":[40],"relevant":[42],"$p_i$,":[43],"enabling":[44],"adaptive":[45],"partial":[49],"sum":[50],"over":[51,140],"this":[52],"interval.":[53],"Unlike":[54],"previous":[55],"variable-time":[56],"approaches,":[57],"our":[58,161],"method":[59],"avoids":[60],"high":[61],"control":[62],"overhead":[63],"and":[64,111,150],"requires":[65],"only":[66],"constant":[67],"extra":[68],"ancilla":[69],"qubits.":[70],"As":[71],"an":[72],"application,":[73],"present":[75],"efficient":[76],"estimators":[78,144,167],"$q$-Tsallis":[81],"entropy":[82],"distributions.":[85],"Specifically:":[86],"(i)":[87],"$q":[89],">":[90],"1$,":[91,126],"obtain":[93,128],"near-optimal":[95,142,165],"algorithm":[97,131],"with":[98,132],"query":[99,133],"complexity":[100,134],"$\\tilde\u0398(1/\\varepsilon^{\\max\\{1/(2(q-1)),":[101],"1\\}})$,":[102],"improving":[103],"prior":[105],"best":[106],"$O(1/\\varepsilon^{1+1/(q-1)})$":[107],"due":[108,145],"Liu":[110],"Wang":[112],"(SODA":[113],"2025;":[114],"IEEE":[115],"Trans.":[116,153],"Inf.":[117,154],"Theory":[118,155],"2026).":[119],"(ii)":[120],"$0":[122],"<":[123,125],"q":[124],"$\\tilde{O}(n^{1/q-1/2}/\\varepsilon^{1/q})$,":[135],"exhibiting":[136],"speedup":[139],"classical":[143],"Jiao,":[147],"Venkat,":[148],"Han,":[149],"Weissman":[151],"(IEEE":[152],"2017).":[156],"Our":[157],"results":[158],"achieve,":[159],"knowledge,":[162],"first":[164],"parameterized":[169],"$q$-entropy":[170],"non-integer":[172],"$q$.":[173]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-07T00:00:00"}