{"id":"https://openalex.org/W7214739086","doi":"https://doi.org/10.48550/arxiv.2609.34532","title":"Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms","display_name":"Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214739086","doi":"https://doi.org/10.48550/arxiv.2609.34532"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34532","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34532","pdf_url":"https://arxiv.org/pdf/2609.34532","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/2609.34532","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023060969","display_name":"Sevag Gharibian","orcid":"https://orcid.org/0000-0002-9992-3379","observed_orcids":["https://orcid.org/0000-0002-9992-3379"]},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gharibian, Sevag","raw_affiliation_strings":["Department of Computer Science and Institute for Photonic Quantum Systems , Paderborn University , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Institute for Photonic Quantum Systems , Paderborn University , Germany","institution_ids":["https://openalex.org/I206945453"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153443180","display_name":"Fran\u00e7ois Le Gall","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gall, Fran\u00e7ois Le","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136491015","display_name":"Ranitha Mataraarachchi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mataraarachchi, Ranitha","raw_affiliation_strings":["Graduate School of Mathematics , Nagoya University , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Mathematics , Nagoya University , Japan","institution_ids":["https://openalex.org/I60134161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112486227","display_name":"Suguru Tamaki","orcid":"https://orcid.org/0000-0002-8105-2368","observed_orcids":["https://orcid.org/0000-0002-8105-2368"]},"institutions":[{"id":"https://openalex.org/I180941496","display_name":"University of Hyogo","ror":"https://ror.org/0151bmh98","country_code":"JP","type":"education","lineage":["https://openalex.org/I180941496"]},{"id":"https://openalex.org/I84059937","display_name":"Hyogo University","ror":"https://ror.org/024pdem44","country_code":"JP","type":"education","lineage":["https://openalex.org/I84059937"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tamaki, Suguru","raw_affiliation_strings":["Graduate School of Information Science , University of Hyogo , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science , University of Hyogo , Japan","institution_ids":["https://openalex.org/I180941496","https://openalex.org/I84059937"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"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":0.9984999895095825,"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":0.9984999895095825,"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":0.0007999999797903001,"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":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/low-energy-states","display_name":"low-energy states","score":0.8450000286102295},{"id":"https://openalex.org/keywords/quantum-state-preparation","display_name":"quantum state preparation","score":0.6480000019073486},{"id":"https://openalex.org/keywords/quantum-algorithms","display_name":"quantum algorithms","score":0.6629999876022339},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"binary entropy function","score":0.8740000128746033},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.6200000047683716},{"id":"https://openalex.org/keywords/depolarization","display_name":"depolarization","score":0.902999997138977},{"id":"https://openalex.org/keywords/heisenberg-model","display_name":"Heisenberg model","score":0.9430000185966492},{"id":"https://openalex.org/keywords/xy-model","display_name":"XY model","score":0.968999981880188},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.9950000047683716},{"id":"https://openalex.org/keywords/interaction-graphs","display_name":"interaction graphs","score":0.7260000109672546},{"id":"https://openalex.org/keywords/quantum-complexity","display_name":"quantum complexity","score":0.5479999780654907}],"concepts":[{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.621399998664856},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6105999946594238},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.579800009727478},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5482000112533569},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.498199999332428},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4553999900817871},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.44909998774528503},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4462999999523163},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43869999051094055},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.42719998955726624},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.40630000829696655},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4027999937534332},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4025000035762787},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.37279999256134033},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3686999976634979},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36469998955726624},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3522999882698059},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.3411000072956085},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.32829999923706055},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3273000121116638},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2987000048160553},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.28610000014305115},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.28529998660087585},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.2703999876976013},{"id":"https://openalex.org/C136269434","wikidata":"https://www.wikidata.org/wiki/Q1502341","display_name":"Quantum chaos","level":4,"score":0.26510000228881836},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2599000036716461},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.251800000667572},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.34532","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34532","pdf_url":"https://arxiv.org/pdf/2609.34532","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.2609.34532","doi":"https://doi.org/10.48550/arxiv.2609.34532","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34532","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:2609.34532","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34532","pdf_url":"https://arxiv.org/pdf/2609.34532","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":[{"id":"https://openalex.org/G1587758330","display_name":null,"funder_award_id":"SPP 2514","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3578047007","display_name":null,"funder_award_id":"JPMJCR24I4","funder_id":"https://openalex.org/F4320338075","funder_display_name":"Core Research for Evolutional Science and Technology"},{"id":"https://openalex.org/G460077191","display_name":"Foundations of Secure Distributed Quantum Computing on Medium-Scale Quantum Computers","funder_award_id":"25K24674","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4627739467","display_name":null,"funder_award_id":"JP-MXS0120319794","funder_id":"https://openalex.org/F4320320912","funder_display_name":"Ministry of Education, Culture, Sports, Science and Technology"},{"id":"https://openalex.org/G6976712858","display_name":"Foundations of Secure Distributed Quantum Computing on Medium-Scale Quantum Computers","funder_award_id":"24H00071","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G9000362279","display_name":null,"funder_award_id":"25K24465","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320912","display_name":"Ministry of Education, Culture, Sports, Science and Technology","ror":"https://ror.org/048rj2z13"},{"id":"https://openalex.org/F4320330828","display_name":"QuantERA","ror":null},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320338075","display_name":"Core Research for Evolutional Science and Technology","ror":"https://ror.org/00097mb19"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214739086.pdf","grobid_xml":"https://content.openalex.org/works/W7214739086.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2088453258","https://openalex.org/W7161727173","https://openalex.org/W7204261529","https://openalex.org/W7204271847"],"related_works":["https://openalex.org/W7161727173","https://openalex.org/W4400376503","https://openalex.org/W3157942663","https://openalex.org/W4385682610","https://openalex.org/W6891903755","https://openalex.org/W4414788683","https://openalex.org/W7170155408","https://openalex.org/W7110132136","https://openalex.org/W335329583","https://openalex.org/W7147114761"],"abstract_inverted_index":{"Low-energy":[0],"estimation":[1],"and":[2,41,130],"state":[3],"preparation":[4],"for":[5,29,54,127],"general":[6],"$k$-local":[7],"Hamiltonians":[8],"are":[9],"fundamental":[10],"challenges":[11],"in":[12,118],"quantum":[13,52],"complexity":[14],"theory.":[15],"Buhrman":[16],"et":[17],"al.~":[18],"[BGLGST,":[19,81],"PRL":[20,82],"2025]":[21],"recently":[22],"broke":[23],"the":[24,33,37,42,58,63,73,94,97,119],"natural":[25],"Grover":[26],"bound":[27,92,111],"$O^\\ast(2^{n/2})$":[28],"both":[30],"problems,":[31,56],"with":[32],"improvement":[34],"depending":[35],"on":[36,93,133],"relative":[38],"accuracy":[39],"$\\varepsilon$":[40],"locality":[43],"$k$.":[44],"In":[45],"this":[46,110],"work,":[47],"we":[48],"present":[49],"faster":[50],"exponential":[51],"algorithms":[53,71],"these":[55],"where":[57],"binary":[59],"entropy":[60],"function":[61],"governs":[62],"runtime":[64],"exponent.":[65,120],"For":[66,107],"sufficiently":[67],"small":[68],"$\\varepsilon/k$,":[69],"our":[70],"improve":[72],"exponent":[74],"by":[75,102],"a":[76],"factor":[77],"of":[78,96],"$\\log(k/\\varepsilon)$":[79],"over":[80],"2025].":[83],"Our":[84],"main":[85],"technical":[86],"result":[87],"is":[88,112],"an":[89],"entropy-governed":[90],"lower":[91],"dimension":[95],"Hamiltonian's":[98],"low-energy":[99],"subspace,":[100],"obtained":[101],"depolarizing":[103],"its":[104],"ground":[105],"state.":[106],"fixed":[108],"$k$,":[109],"optimal":[113],"up":[114],"to":[115],"constant":[116],"factors":[117],"The":[121],"same":[122],"framework":[123],"yields":[124],"tighter":[125],"bounds":[126],"Heisenberg,":[128],"$XY$,":[129],"Ising":[131],"models":[132],"arbitrary":[134],"interaction":[135],"graphs.":[136]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}