{"id":"https://openalex.org/W4414815938","doi":"https://doi.org/10.48550/arxiv.2510.01333","title":"Derandomised tensor product gap amplification for quantum Hamiltonians","display_name":"Derandomised tensor product gap amplification for quantum Hamiltonians","publication_year":2025,"publication_date":"2025-10-01","ids":{"openalex":"https://openalex.org/W4414815938","doi":"https://doi.org/10.48550/arxiv.2510.01333"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2510.01333","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.01333","pdf_url":"https://arxiv.org/pdf/2510.01333","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.01333","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042625492","display_name":"Thiago Bergamaschi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bergamaschi, Thiago","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055932754","display_name":"Tony Metger","orcid":"https://orcid.org/0000-0002-3108-8100"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Metger, Tony","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019616211","display_name":"Thomas Vidick","orcid":"https://orcid.org/0000-0002-6405-365X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vidick, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108825718","display_name":"Tina Zhang","orcid":"https://orcid.org/0000-0002-7229-6686"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Tina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"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/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9510999917984009,"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"}},"topics":[{"id":"https://openalex.org/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9510999917984009,"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/T13650","display_name":"Computational Physics and Python Applications","score":0.9484999775886536,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9453999996185303,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/tensor-product","display_name":"Tensor product","score":0.7414000034332275},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.6279000043869019},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5806999802589417},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4763999879360199},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.39430001378059387},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.3488999903202057}],"concepts":[{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.7414000034332275},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6279000043869019},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5806999802589417},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5167999863624573},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.498199999332428},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4763999879360199},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4041999876499176},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.34850001335144043},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31520000100135803},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.296999990940094},{"id":"https://openalex.org/C122527463","wikidata":"https://www.wikidata.org/wiki/Q578430","display_name":"Quantum decoherence","level":3,"score":0.29580000042915344},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.27320000529289246},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.2612000107765198}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.01333","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.01333","pdf_url":"https://arxiv.org/pdf/2510.01333","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2510.01333","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.01333","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":"pmh:oai:arXiv.org:2510.01333","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.01333","pdf_url":"https://arxiv.org/pdf/2510.01333","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"quantum":[1,94,130,146],"PCP":[2,82,147],"conjecture":[3],"asks":[4],"whether":[5],"it":[6],"is":[7,25,32,51,72],"QMA-hard":[8],"to":[9,46,59,107,139,144],"distinguish":[10,47],"between":[11,20],"high-":[12,40],"and":[13,22,41,55],"low-energy":[14,42],"Hamiltonians":[15,43,58,99],"even":[16],"when":[17],"the":[18,37,49,57,61,74,80,110,113,145],"gap":[19,33,50,63,69,95],"\"high\"":[21],"\"low\"":[23],"energy":[24,62],"large":[26],"(constant).":[27],"A":[28],"natural":[29],"proof":[30,78],"strategy":[31],"amplification:":[34],"start":[35],"from":[36],"fact":[38],"that":[39],"are":[44],"hard":[45],"if":[48],"small":[52],"(inverse":[53],"polynomial)":[54],"amplify":[56],"increase":[60],"while":[64],"preserving":[65],"hardness.":[66],"Such":[67],"a":[68,92,118,125],"amplification":[70,96,116],"procedure":[71,97],"at":[73],"heart":[75],"of":[76,79,117],"Dinur's":[77,88],"classical":[81],"theorem.":[83],"In":[84],"this":[85],"work,":[86],"following":[87],"model,":[89],"we":[90],"introduce":[91],"new":[93,126],"for":[98],"which":[100,134],"uses":[101],"random":[102],"walks":[103],"on":[104,124],"expander":[105],"graphs":[106],"derandomise":[108],"(subsample":[109],"terms":[111],"of)":[112],"tensor":[114],"product":[115],"Hamiltonian.":[119],"Curiously,":[120],"our":[121],"analysis":[122],"relies":[123],"technique":[127],"inspired":[128],"by":[129],"de":[131],"Finetti":[132],"theorems,":[133],"have":[135],"previously":[136],"been":[137],"used":[138],"rule":[140],"out":[141],"certain":[142],"approaches":[143],"conjecture.":[148]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
