{"id":"https://openalex.org/W7216594480","doi":"https://doi.org/10.48550/arxiv.2610.01141","title":"Classical Hardness of Learning Functions of Hamiltonians","display_name":"Classical Hardness of Learning Functions of Hamiltonians","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216594480","doi":"https://doi.org/10.48550/arxiv.2610.01141"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.01141","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01141","pdf_url":"https://arxiv.org/pdf/2610.01141","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/2610.01141","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5155855447","display_name":"Sota Hashimoto","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I178574317","display_name":"Mie University","ror":"https://ror.org/01529vy56","country_code":"JP","type":"education","lineage":["https://openalex.org/I178574317"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hashimoto, Sota","raw_affiliation_strings":["Graduate School of Engineering , Mie University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering , Mie University ,","institution_ids":["https://openalex.org/I178574317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024624998","display_name":"Akinori Kawachi","orcid":"https://orcid.org/0000-0001-9218-9944","observed_orcids":["https://orcid.org/0000-0001-9218-9944"]},"institutions":[{"id":"https://openalex.org/I178574317","display_name":"Mie University","ror":"https://ror.org/01529vy56","country_code":"JP","type":"education","lineage":["https://openalex.org/I178574317"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kawachi, Akinori","raw_affiliation_strings":["Graduate School of Engineering , Mie University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering , Mie University ,","institution_ids":["https://openalex.org/I178574317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I178574317"],"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":0.9951000213623047,"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":0.9951000213623047,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.0013000000035390258,"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/T10237","display_name":"Cryptography and Data Security","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-machine-learning","display_name":"quantum machine learning","score":0.9309999942779541},{"id":"https://openalex.org/keywords/average-case-hardness","display_name":"average-case hardness","score":0.7310000061988831},{"id":"https://openalex.org/keywords/squared-error-loss","display_name":"squared error loss","score":0.4790000021457672},{"id":"https://openalex.org/keywords/polynomial-time-algorithms","display_name":"polynomial-time algorithms","score":0.43299999833106995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6790000200271606},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6662999987602234},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5116999745368958},{"id":"https://openalex.org/C177225278","wikidata":"https://www.wikidata.org/wiki/Q192674","display_name":"Factoring","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3736000061035156},{"id":"https://openalex.org/C192353077","wikidata":"https://www.wikidata.org/wiki/Q4682635","display_name":"Adiabatic quantum computation","level":4,"score":0.3472000062465668},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33739998936653137},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.31060001254081726},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.3041999936103821},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.2946000099182129},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2775000035762787},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26159998774528503},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.2574000060558319},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.01141","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01141","pdf_url":"https://arxiv.org/pdf/2610.01141","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.2610.01141","doi":"https://doi.org/10.48550/arxiv.2610.01141","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.01141","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:2610.01141","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01141","pdf_url":"https://arxiv.org/pdf/2610.01141","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/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7216594480.pdf","grobid_xml":"https://content.openalex.org/works/W7216594480.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4382618821","https://openalex.org/W4415065700","https://openalex.org/W4417539632"],"related_works":["https://openalex.org/W4415065700","https://openalex.org/W4414647710","https://openalex.org/W4382618821","https://openalex.org/W4417539632","https://openalex.org/W4309582570","https://openalex.org/W2101429643","https://openalex.org/W2921611845","https://openalex.org/W1987965590","https://openalex.org/W3020405832","https://openalex.org/W3138650000"],"abstract_inverted_index":{"Morohoshi,":[0],"Nakayama,":[1],"Manabe,":[2],"and":[3,32,92],"Mitarai":[4],"proposed":[5],"a":[6,29,33,65,141],"physically":[7],"motivated":[8],"quantum":[9,34,57],"machine":[10],"learning":[11,49,58,88],"problem":[12,46,138],"in":[13,50,95,132],"which":[14],"the":[15,22,79,96,103,106],"goal":[16],"is":[17,39],"to":[18],"predict":[19],"quantities":[20],"of":[21,28,68,98,105,109],"form":[23],"$\\operatorname{Tr}[f(H)\u03c1]$":[24],"from":[25],"classical":[26,70,81,121,133,142],"descriptions":[27],"Hamiltonian":[30,47,86],"$H$":[31],"state":[35],"$\u03c1$,":[36],"where":[37],"$f$":[38],"an":[40,55,119],"unknown":[41],"function.":[42],"We":[43],"call":[44],"this":[45,51,74],"function":[48,87],"paper.":[52],"They":[53],"constructed":[54],"efficient":[56,120],"algorithm":[59,145],"under":[60,102,124],"suitable":[61],"conditions,":[62],"while":[63],"leaving":[64],"rigorous":[66],"proof":[67],"average-case":[69,80,107],"hardness":[71,82,108],"open.":[72],"In":[73],"paper,":[75],"we":[76,116],"rigorously":[77],"prove":[78],"for":[83,90,136,146],"two":[84],"distribution-specific":[85],"problems":[89],"$f_{\\cos,\u03c0}(\u03bb)=\\cos(\u03c0\u03bb)$":[91],"$f_{\\exp,\u03b2}(\u03bb)=e^{-\u03b2\u03bb}$":[93],"discussed":[94],"paper":[97],"Morohoshi":[99],"et":[100],"al.":[101],"assumption":[104],"factoring":[110,147],"random":[111,148],"RSA":[112,149],"moduli.":[113,150],"More":[114],"specifically,":[115],"show":[117],"that":[118],"randomized":[122,143],"learner":[123],"squared":[125],"loss":[126],"whose":[127],"output":[128],"hypotheses":[129],"are":[130],"evaluable":[131],"polynomial":[134],"time":[135],"either":[137],"would":[139],"yield":[140],"polynomial-time":[144]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}
