{"id":"https://openalex.org/W7213606262","doi":"https://doi.org/10.48550/arxiv.2609.20253","title":"Quantum Speedups for Log-Concave Sampling from Local Structure","display_name":"Quantum Speedups for Log-Concave Sampling from Local Structure","publication_year":2026,"publication_date":"2026-08-14","ids":{"openalex":"https://openalex.org/W7213606262","doi":"https://doi.org/10.48550/arxiv.2609.20253"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20253","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20253","pdf_url":"https://arxiv.org/pdf/2609.20253","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/2609.20253","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152150697","display_name":"Chenghua Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Chenghua","raw_affiliation_strings":["Institute of Software , Chinese Academy of Sciences , Beijing , China","University of Chinese Academy of Sciences , Beijing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Software , Chinese Academy of Sciences , Beijing , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences , Beijing , China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5143625400","display_name":"Qisheng Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Qisheng","raw_affiliation_strings":["School of Computer Science , Shanghai Jiao Tong University , Shanghai , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science , Shanghai Jiao Tong University , Shanghai , China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043930796","display_name":"Zhengfeng Ji","orcid":"https://orcid.org/0000-0002-7659-3178","observed_orcids":["https://orcid.org/0000-0002-7659-3178"]},"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":"Ji, Zhengfeng","raw_affiliation_strings":["Department of Computer Science and Technology , Tsinghua University , Beijing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology , Tsinghua University , Beijing , China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9980000257492065,"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":0.9980000257492065,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.000699999975040555,"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"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":9.999999747378752e-05,"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-algorithms","display_name":"quantum algorithms","score":0.7429999709129333},{"id":"https://openalex.org/keywords/condition-number","display_name":"condition number","score":0.7350000143051147},{"id":"https://openalex.org/keywords/gaussian-markov-random-fields","display_name":"Gaussian Markov random fields","score":0.800000011920929},{"id":"https://openalex.org/keywords/high-dimensional-sampling","display_name":"high-dimensional sampling","score":0.8539999723434448},{"id":"https://openalex.org/keywords/quantum-advantage","display_name":"quantum advantage","score":0.4009999930858612}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5378000140190125},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5196999907493591},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.492000013589859},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4747999906539917},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4668000042438507},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4528999924659729},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.42750000953674316},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.3686999976634979},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36000001430511475},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3596000075340271},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.3537999987602234},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.35370001196861267},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.34779998660087585},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.3321000039577484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3260999917984009},{"id":"https://openalex.org/C62641251","wikidata":"https://www.wikidata.org/wiki/Q7269097","display_name":"Quantum sort","level":5,"score":0.3190000057220459},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.31060001254081726},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.30820000171661377},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.29899999499320984},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2921000123023987},{"id":"https://openalex.org/C170593435","wikidata":"https://www.wikidata.org/wiki/Q4128565","display_name":"Slice sampling","level":4,"score":0.2842000126838684},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2721000015735626},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.26030001044273376},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2565999925136566},{"id":"https://openalex.org/C2986090443","wikidata":"https://www.wikidata.org/wiki/Q77870413","display_name":"Local structure","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20253","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20253","pdf_url":"https://arxiv.org/pdf/2609.20253","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.2609.20253","doi":"https://doi.org/10.48550/arxiv.2609.20253","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20253","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.20253","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20253","pdf_url":"https://arxiv.org/pdf/2609.20253","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213606262.pdf","grobid_xml":"https://content.openalex.org/works/W7213606262.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4364387748","https://openalex.org/W4403821519","https://openalex.org/W4415980706"],"related_works":["https://openalex.org/W7133211409","https://openalex.org/W4362679655","https://openalex.org/W3168466603","https://openalex.org/W3092103854","https://openalex.org/W4407386472","https://openalex.org/W6922538077","https://openalex.org/W4416091653","https://openalex.org/W4415980706","https://openalex.org/W4414946066","https://openalex.org/W4415232647"],"abstract_inverted_index":{"For":[0],"a":[1,14,34,81,88,140,183],"convex":[2],"function":[3,28],"$f":[4],"\\colon":[5],"\\mathbb{R}^d":[6],"\\to":[7],"\\mathbb{R}$,":[8],"the":[9,27,67,102,107,123],"problem":[10],"of":[11,84,143],"sampling":[12,47,94],"from":[13,147],"distribution":[15],"proportional":[16],"to":[17,32,56,69,114,139],"$e^{-f(x)}$":[18],"is":[19,87,101,176],"called":[20],"log-concave":[21,46,93],"sampling.":[22,189],"In":[23,41],"many":[24],"practical":[25],"scenarios,":[26],"$f(x)$":[29,70],"turns":[30],"out":[31],"admit":[33],"local":[35,49,97,174],"decomposition":[36],"$f(x)":[37],"=":[38],"\\sum_{a=1}^R":[39],"\u03c8_a(x_{S_a})$.":[40],"this":[42],"paper,":[43],"we":[44],"consider":[45],"using":[48,95],"queries,":[50,98],"i.e.,":[51],"evaluation":[52],"and":[53,117,122,150,165],"gradient":[54],"queries":[55,68],"each":[57,76],"clause":[58],"$\u03c8_a(\\cdot)$,":[59],"which":[60],"can":[61],"be":[62],"computationally":[63],"much":[64],"cheaper":[65],"than":[66],"itself.":[71],"We":[72],"show":[73],"that":[74,173],"if":[75],"coordinate":[77],"appears":[78],"in":[79],"only":[80],"small":[82],"number":[83],"clauses,":[85],"there":[86],"quantum":[89,124,136,184],"algorithm":[90],"for":[91,187],"strongly":[92],"$\\widetilde{O}(\\sqrt\u03bad)$":[96],"where":[99],"$\u03ba$":[100],"condition":[103],"number.":[104],"This":[105],"improves":[106],"prior":[108],"best":[109],"classical":[110],"result":[111,125],"$\\widetilde{O}(\u03bad)$":[112],"due":[113],"Ascolani,":[115],"Lavenant,":[116],"Zanella":[118],"(Ann.":[119],"Probab.":[120],"2026)":[121],"$\\widetilde{O}(\\sqrt\u03ba":[126],"d^2)$":[127],"implied":[128],"by":[129],"Childs":[130],"et":[131],"al.":[132],"(NeurIPS":[133],"2022).":[134],"Our":[135],"sampler":[137],"applies":[138],"broad":[141],"class":[142],"locally":[144],"structured":[145],"models":[146],"statistical":[148],"computing":[149],"machine":[151],"learning,":[152],"with":[153],"representative":[154],"examples":[155],"including":[156],"Gaussian":[157,163],"Markov":[158],"random":[159],"fields,":[160],"finite-element":[161],"latent":[162],"models,":[164],"sparse":[166],"generalized":[167],"linear":[168],"models.":[169],"These":[170],"results":[171],"demonstrate":[172],"structure":[175],"not":[177],"merely":[178],"an":[179],"implementation":[180],"detail,":[181],"but":[182],"algorithmic":[185],"resource":[186],"high-dimensional":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}
