{"id":"https://openalex.org/W7220714245","doi":"https://doi.org/10.48550/arxiv.2610.04952","title":"Gap Amplification for Local Hamiltonians with Combinatorial Soundness","display_name":"Gap Amplification for Local Hamiltonians with Combinatorial Soundness","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220714245","doi":"https://doi.org/10.48550/arxiv.2610.04952"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04952","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04952","pdf_url":"https://arxiv.org/pdf/2610.04952","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/2610.04952","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039083557","display_name":"Mitali Bafna","orcid":"https://orcid.org/0000-0002-3003-2017","observed_orcids":["https://orcid.org/0000-0002-3003-2017"]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bafna, Mitali","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046796538","display_name":"Quynh T. Nguyen","orcid":"https://orcid.org/0000-0002-6495-4394","observed_orcids":["https://orcid.org/0000-0002-6495-4394"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nguyen, Quynh T.","raw_affiliation_strings":["Harvard & UC Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard & UC Berkeley","institution_ids":["https://openalex.org/I136199984","https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108825718","display_name":"Tina Zhang","orcid":"https://orcid.org/0000-0002-7229-6686","observed_orcids":["https://orcid.org/0000-0002-7229-6686"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhang, Tina","raw_affiliation_strings":["MIT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"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":0.9794999957084656,"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":0.9794999957084656,"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":0.00989999994635582,"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":0.0038999998942017555,"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/local-hamiltonians","display_name":"local Hamiltonians","score":0.9309999942779541},{"id":"https://openalex.org/keywords/fault-tolerant-computation","display_name":"fault-tolerant computation","score":0.8859999775886536},{"id":"https://openalex.org/keywords/high-dimensional-expanders","display_name":"high-dimensional expanders","score":0.8569999933242798},{"id":"https://openalex.org/keywords/qudits","display_name":"qudits","score":0.6660000085830688}],"concepts":[{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.6331999897956848},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6305999755859375},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.5730000138282776},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5184000134468079},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4442000091075897},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.423799991607666},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4140999913215637},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3921999931335449},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3693000078201294},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.36820000410079956},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.36320000886917114},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.362199991941452},{"id":"https://openalex.org/C190463098","wikidata":"https://www.wikidata.org/wiki/Q2081419","display_name":"Quantum technology","level":4,"score":0.34470000863075256},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.33469998836517334},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.3321000039577484},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3109999895095825},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.299699991941452},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.29760000109672546},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.28459998965263367},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.2793999910354614},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.271699994802475},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C2984281365","wikidata":"https://www.wikidata.org/wiki/Q906781","display_name":"Quantum control","level":3,"score":0.2581000030040741},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.257099986076355},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2565999925136566},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2563000023365021},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04952","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04952","pdf_url":"https://arxiv.org/pdf/2610.04952","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.2610.04952","doi":"https://doi.org/10.48550/arxiv.2610.04952","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04952","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:2610.04952","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04952","pdf_url":"https://arxiv.org/pdf/2610.04952","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":[{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220714245.pdf","grobid_xml":"https://content.openalex.org/works/W7220714245.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2128164182","https://openalex.org/W4414815938","https://openalex.org/W4415194899"],"related_works":["https://openalex.org/W4414815938","https://openalex.org/W2007370826","https://openalex.org/W4412203675","https://openalex.org/W7100353575","https://openalex.org/W4321853643","https://openalex.org/W2126382599","https://openalex.org/W4393064103","https://openalex.org/W2039104910","https://openalex.org/W4404350854","https://openalex.org/W2259833267"],"abstract_inverted_index":{"The":[0],"quantum":[1,12,44,48,128,154,178,210],"PCP":[2,31,114,190],"conjecture":[3],"is":[4,53,101],"one":[5,168],"of":[6,28,79,93,106,142,159,169,191,201],"the":[7,26,29,77,80,96,104,112,122,139,170,177,187,198],"major":[8],"open":[9],"problems":[10],"in":[11,19,25,157,173,203,209],"complexity":[13],"theory.":[14,212],"It":[15],"has":[16],"resisted":[17],"attack":[18],"part":[20],"because":[21],"many":[22,107],"primitives":[23],"used":[24],"proof":[27],"classical":[30,113,174,189],"theorem,":[32],"such":[33],"as":[34,58],"locality-preserving":[35,129],"gap":[36,51,99,130,141,155],"amplification":[37,52,100,156],"and":[38,65,82,132,162,197],"alphabet":[39],"reduction,":[40],"have":[41],"no":[42],"obvious":[43],"analogues":[45],"due":[46],"to":[47,103,205],"no-cloning.":[49],"Locality-preserving":[50],"a":[54,60,67,71,148,164],"procedure":[55,137],"that":[56,135],"takes":[57],"input":[59],"local":[61,87,143],"Hamiltonian":[62],"problem":[63],"instance":[64,69],"produces":[66],"new":[68,149],"with":[70],"larger":[72],"promise":[73],"gap,":[74],"without":[75],"increasing":[76,85],"locality":[78,97],"Hamiltonian,":[81],"instead":[83],"moderately":[84],"its":[86],"qudit":[88],"dimension.":[89],"Obtaining":[90],"this":[91,117],"kind":[92],"control":[94],"over":[95],"during":[98],"critical":[102],"success":[105],"known":[108,124],"strategies":[109],"for":[110,127,151],"proving":[111],"theorem.":[115],"In":[116,180],"work,":[118],"we":[119,133,182],"put":[120],"forth":[121],"first":[123],"viable":[125],"template":[126],"amplification,":[131],"prove":[134],"our":[136],"amplifies":[138],"combinatorial":[140],"Hamiltonians.":[144],"Our":[145],"work":[146],"introduces":[147],"framework":[150],"reasoning":[152],"about":[153],"terms":[158],"fault-tolerant":[160],"computation,":[161],"illuminates":[163],"route":[165],"toward":[166],"importing":[167],"central":[171],"ingredients":[172],"PCPs":[175],"into":[176],"setting.":[179],"particular,":[181],"build":[183],"upon":[184],"ideas":[185],"from":[186],"recent":[188,207],"Bafna--Minzer--Vyas":[192],"based":[193],"on":[194],"high-dimensional":[195],"expanders,":[196],"circuit-to-Hamiltonian":[199],"construction":[200],"Anshu--Breuckmann--Nguyen,":[202],"addition":[204],"several":[206],"advances":[208],"coding":[211]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
