{"id":"https://openalex.org/W7213743193","doi":"https://doi.org/10.48550/arxiv.2610.00112","title":"Local Anticoncentration for Gaussian Boson Sampling via Conditional Wishart Geometry","display_name":"Local Anticoncentration for Gaussian Boson Sampling via Conditional Wishart Geometry","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7213743193","doi":"https://doi.org/10.48550/arxiv.2610.00112"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.00112","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00112","pdf_url":"https://arxiv.org/pdf/2610.00112","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/2610.00112","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016307489","display_name":"Hongru Zhao","orcid":"https://orcid.org/0000-0002-1753-4709","observed_orcids":["https://orcid.org/0000-0002-1753-4709"]},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhao, Hongru","raw_affiliation_strings":["School of Statistics , University of Minnesota , Minneapolis , Minnesota , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics , University of Minnesota , Minneapolis , Minnesota , USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016307489"],"corresponding_institution_ids":["https://openalex.org/I130238516"],"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":0.8476999998092651,"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":0.8476999998092651,"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/T11716","display_name":"Random Matrices and Applications","score":0.06880000233650208,"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/T11166","display_name":"Analytic Number Theory Research","score":0.009200000204145908,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/gaussian-boson-sampling","display_name":"Gaussian boson sampling","score":0.8880000114440918},{"id":"https://openalex.org/keywords/anti-concentration","display_name":"anti-concentration","score":0.8659999966621399},{"id":"https://openalex.org/keywords/small-ball-probabilities","display_name":"small ball probabilities","score":0.7900000214576721},{"id":"https://openalex.org/keywords/hafnian","display_name":"hafnian","score":0.8960000276565552},{"id":"https://openalex.org/keywords/quantum-advantage","display_name":"quantum advantage","score":0.8679999709129333},{"id":"https://openalex.org/keywords/quantum-complexity","display_name":"quantum complexity","score":0.34700000286102295},{"id":"https://openalex.org/keywords/lean-formal-verification","display_name":"Lean formal verification","score":0.5230000019073486}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7524999976158142},{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.6025000214576721},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5979999899864197},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.539900004863739},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48190000653266907},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.42899999022483826},{"id":"https://openalex.org/C200106649","wikidata":"https://www.wikidata.org/wiki/Q223683","display_name":"Transpose","level":3,"score":0.4255000054836273},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3880999982357025},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3637999892234802},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.35339999198913574},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.34040001034736633},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.3100000023841858},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.30480000376701355},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.28130000829696655},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26570001244544983},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25540000200271606}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2610.00112","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00112","pdf_url":"https://arxiv.org/pdf/2610.00112","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.2610.00112","doi":"https://doi.org/10.48550/arxiv.2610.00112","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.00112","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"},{"id":"doi:10.5281/zenodo.22856032","doi":"https://doi.org/10.5281/zenodo.22856032","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22856032","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.22856033","doi":"https://doi.org/10.5281/zenodo.22856033","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22856033","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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:2610.00112","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00112","pdf_url":"https://arxiv.org/pdf/2610.00112","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/W7213743193.pdf","grobid_xml":"https://content.openalex.org/works/W7213743193.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W2085398078","https://openalex.org/W2215006509","https://openalex.org/W2560356194","https://openalex.org/W2784845971","https://openalex.org/W2949591539","https://openalex.org/W4409247852","https://openalex.org/W4409262713","https://openalex.org/W7154698176","https://openalex.org/W7170136473","https://openalex.org/W7203783923","https://openalex.org/W7206197862"],"related_works":["https://openalex.org/W7214787576","https://openalex.org/W7203783923","https://openalex.org/W4393113523","https://openalex.org/W7171422102","https://openalex.org/W7206197862","https://openalex.org/W4409247852","https://openalex.org/W4409262713","https://openalex.org/W3205206051","https://openalex.org/W7166646635","https://openalex.org/W7212030173"],"abstract_inverted_index":{"Anticoncentration":[0],"is":[1],"a":[2,35],"key":[3],"ingredient":[4],"in":[5],"complexity":[6],"theoretic":[7],"arguments":[8],"for":[9,23,53,79],"quantum":[10],"advantage":[11],"from":[12],"Gaussian":[13,25,32,45,72],"boson":[14],"sampling.":[15],"Here":[16],"we":[17,47],"prove":[18],"polynomial":[19,49,74,90,99],"small":[20,50,75,100,119],"ball":[21,51,76,101],"anticoncentration":[22,52,77,113],"complex":[24,30,44,70],"transpose":[26],"Gram":[27],"hafnians":[28,65],"and":[29,59,149,159],"symmetric":[31,71],"hafnians.":[33],"For":[34,64],"k":[36,56],"\u00d7":[37,68],"2n":[38,67,69],"matrix":[39],"X":[40],"with":[41,96,127],"independent":[42],"standard":[43],"entries,":[46],"establish":[48],"haf(X\u1d40X)":[54],"under":[55],"\u2265":[57,82],"4n":[58],"n\u00b2/k":[60],"=":[61],"O(log":[62],"n).":[63],"of":[66,118],"matrices,":[73],"holds":[78],"every":[80],"n":[81],"1.":[83],"In":[84],"both":[85],"ensembles,":[86],"any":[87],"prescribed":[88],"inverse":[89,98],"failure":[91],"probability":[92,117],"can":[93],"be":[94],"achieved":[95],"an":[97],"radius,":[102],"uniformly":[103],"over":[104],"all":[105],"centers.":[106],"These":[107],"results":[108,151],"go":[109],"beyond":[110],"moment":[111],"based":[112],"by":[114],"controlling":[115],"the":[116,139,146],"hafnian":[120,134],"amplitudes.":[121],"The":[122],"proof":[123],"combines":[124],"Fourier":[125],"compression":[126],"conditional":[128],"Wishart":[129],"geometry":[130],"to":[131],"handle":[132],"dependent":[133],"cofactors.":[135],"Files:":[136],"main.pdf":[137],"contains":[138,145],"main":[140],"article":[141],"(14":[142],"pages);":[143],"supplement.pdf":[144],"supplementary":[147],"proofs":[148],"additional":[150],"(33":[152],"pages).":[153],"Related":[154],"Lean":[155],"verification":[156],"sources:":[157],"https://doi.org/10.5281/zenodo.22554594":[158],"https://github.com/HongruZhao/ComplexGramHafnians.":[160]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-21T00:00:00"}