{"id":"https://openalex.org/W7214110293","doi":"https://doi.org/10.48550/arxiv.2609.26596","title":"Hamiltonian Learning and Certification via Eigenphase Engineering","display_name":"Hamiltonian Learning and Certification via Eigenphase Engineering","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214110293","doi":"https://doi.org/10.48550/arxiv.2609.26596"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.26596","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26596","pdf_url":"https://arxiv.org/pdf/2609.26596","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/2609.26596","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014120082","display_name":"Myeongjin Shin","orcid":"https://orcid.org/0000-0002-8246-6300","observed_orcids":["https://orcid.org/0000-0002-8246-6300"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR","US"],"is_corresponding":false,"raw_author_name":"Shin, Myeongjin","raw_affiliation_strings":["Institute for Quantum Information and Matter , California Institute of Technology , Pasadena , CA 91125 , USA","School of Computing , Korea Advanced Institute of Science and Technology (KAIST) , Daejeon 34141 , Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Information and Matter , California Institute of Technology , Pasadena , CA 91125 , USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"School of Computing , Korea Advanced Institute of Science and Technology (KAIST) , Daejeon 34141 , Republic of Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108142004","display_name":"Yu Tong","orcid":"https://orcid.org/0000-0002-7555-9373","observed_orcids":["https://orcid.org/0000-0002-7555-9373"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tong, Yu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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":0.9976000189781189,"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":0.9976000189781189,"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":0.0010000000474974513,"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":0.000699999975040555,"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/hamiltonian-learning","display_name":"Hamiltonian learning","score":0.9900000095367432},{"id":"https://openalex.org/keywords/sparse-hamiltonians","display_name":"sparse Hamiltonians","score":0.746999979019165},{"id":"https://openalex.org/keywords/phase-estimation","display_name":"phase estimation","score":0.6930000185966492},{"id":"https://openalex.org/keywords/quantum-machine-learning","display_name":"quantum machine learning","score":0.3179999887943268}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6830000281333923},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.5421000123023987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48330000042915344},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4083999991416931},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38269999623298645},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.37599998712539673},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C192353077","wikidata":"https://www.wikidata.org/wiki/Q4682635","display_name":"Adiabatic quantum computation","level":4,"score":0.3732999861240387},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3621000051498413},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35580000281333923},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.35370001196861267},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30070000886917114},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26750001311302185},{"id":"https://openalex.org/C188116033","wikidata":"https://www.wikidata.org/wiki/Q2664563","display_name":"Q-learning","level":3,"score":0.2669999897480011},{"id":"https://openalex.org/C106553664","wikidata":"https://www.wikidata.org/wiki/Q1156744","display_name":"Time evolution","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25929999351501465},{"id":"https://openalex.org/C46304622","wikidata":"https://www.wikidata.org/wiki/Q374814","display_name":"Certification","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.26596","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26596","pdf_url":"https://arxiv.org/pdf/2609.26596","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.2609.26596","doi":"https://doi.org/10.48550/arxiv.2609.26596","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.26596","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:2609.26596","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26596","pdf_url":"https://arxiv.org/pdf/2609.26596","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/G697302361","display_name":null,"funder_award_id":"DE-SC0025572","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320309398","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055"},{"id":"https://openalex.org/F4320324161","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214110293.pdf","grobid_xml":"https://content.openalex.org/works/W7214110293.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2112543875","https://openalex.org/W4414591995","https://openalex.org/W7124425350","https://openalex.org/W7143451039","https://openalex.org/W7147114761","https://openalex.org/W7165355277","https://openalex.org/W7213441060"],"related_works":["https://openalex.org/W4404307568","https://openalex.org/W4414591995","https://openalex.org/W4417114459","https://openalex.org/W4414788683","https://openalex.org/W4404849502","https://openalex.org/W4415502896","https://openalex.org/W4404340987","https://openalex.org/W4416068656","https://openalex.org/W7159584282","https://openalex.org/W4382726830"],"abstract_inverted_index":{"We":[0],"study":[1],"Hamiltonian":[2,53,191,218],"learning":[3,37,181],"for":[4,153,183],"$k$-local":[5],"Hamiltonians":[6],"at":[7,16],"large":[8],"step":[9,40,84,172],"size,":[10],"using":[11,165],"only":[12,166],"forward":[13],"time":[14,22,73,182],"evolution":[15,72,156],"integer":[17],"multiples":[18],"of":[19,106,133,135,195],"a":[20,39,82,103,175,196,213],"fixed":[21,55],"interval.":[23],"For":[24,49],"this":[25],"task,":[26],"our":[27,60,100],"new":[28],"technique,":[29],"which":[30],"we":[31,91],"call":[32],"eigenphase":[33,210],"engineering,":[34],"achieves":[35],"Heisenberg-limited":[36],"with":[38,54,174,220],"size":[41,85,173],"that":[42],"is":[43],"optimal":[44],"up":[45],"to":[46,66,97,216],"logarithmic":[47],"factors.":[48],"an":[50,88],"unknown":[51,122],"$s$-sparse":[52],"locality":[56,203],"$k$":[57],"and":[58,146,193],"$\\|H\\|_{\\mathrm{op}}\\leq\u039b$,":[59],"algorithm":[61,101],"recovers":[62],"its":[63],"Pauli":[64,198],"coefficients":[65],"$\\ell_2$":[67,180],"error":[68],"$\\varepsilon$":[69],"in":[70,129,179],"total":[71],"$\\widetilde{O}(s/\\varepsilon)$,":[74],"matching":[75],"the":[76,93,121,130,136,151,159,170,200],"best":[77],"known":[78],"scaling":[79],"while":[80],"allowing":[81],"near-maximal":[83],"$\\widetilde\u0398(1/\u039b)$.":[86],"As":[87],"independent":[89],"contribution,":[90],"strengthen":[92],"evolution-time":[94],"lower":[95],"bound":[96],"$\u03a9_k(s^{1-1/(2k)}/\\varepsilon)$,":[98],"placing":[99],"within":[102],"factor":[104],"$\\widetilde{O}(s^{1/(2k)})$":[105],"being":[107],"optimal.":[108],"Eigenphase":[109],"engineering":[110,211],"departs":[111],"from":[112],"approaches":[113],"based":[114],"on":[115],"dynamical":[116],"approximation":[117],"or":[118,204],"iteratively":[119],"canceling":[120],"Hamiltonian.":[123],"It":[124],"encodes":[125],"energy":[126],"expectation":[127],"differences":[128],"perturbative":[131],"response":[132],"eigenphases":[134],"actual":[137],"controlled":[138],"evolution,":[139],"then":[140],"extracts":[141],"them":[142],"through":[143],"phase":[144],"estimation":[145,194],"high-order":[147],"extrapolation.":[148],"This":[149],"avoids":[150],"need":[152],"polynomially":[154],"shorter":[155],"steps":[157],"as":[158,212],"target":[160],"precision":[161],"improves.":[162],"A":[163],"version":[164],"single-qubit":[167],"operations":[168],"retains":[169],"same":[171],"$\\sqrt":[176],"n$":[177],"overhead":[178],"$n$":[184],"qubits.":[185],"The":[186],"method":[187],"also":[188],"enables":[189],"tolerant":[190],"certification":[192],"specified":[197],"coefficient,":[199],"latter":[201],"without":[202],"sparsity":[205],"assumptions.":[206],"These":[207],"results":[208],"establish":[209],"versatile":[214],"approach":[215],"extracting":[217],"information":[219],"infrequent":[221],"control.":[222]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}