{"id":"https://openalex.org/W7214305672","doi":"https://doi.org/10.48550/arxiv.2609.28999","title":"On the numerical limitations of dual Koopman von Neumann embeddings for solving conservative nonlinear ordinary differential equations on quantum computers","display_name":"On the numerical limitations of dual Koopman von Neumann embeddings for solving conservative nonlinear ordinary differential equations on quantum computers","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214305672","doi":"https://doi.org/10.48550/arxiv.2609.28999"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.28999","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28999","pdf_url":"https://arxiv.org/pdf/2609.28999","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/2609.28999","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087286438","display_name":"Thibault Fredon","orcid":"https://orcid.org/0009-0005-9427-9309","observed_orcids":["https://orcid.org/0009-0005-9427-9309"]},"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":"Fredon, Thibault","raw_affiliation_strings":["Plasma Science and Fusion Center , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Plasma Science and Fusion Center , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054576414","display_name":"Abhay K. Ram","orcid":"https://orcid.org/0000-0001-9693-0111","observed_orcids":["https://orcid.org/0000-0001-9693-0111"]},"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":"Ram, Abhay K.","raw_affiliation_strings":["Plasma Science and Fusion Center , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Plasma Science and Fusion Center , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035578344","display_name":"Fabrice Debbasch","orcid":"https://orcid.org/0000-0001-6894-6159","observed_orcids":["https://orcid.org/0000-0001-6894-6159"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I2800004676","display_name":"Observatoire de Paris","ror":"https://ror.org/029nkcm90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2746051580","https://openalex.org/I2800004676"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Debbasch, Fabrice","raw_affiliation_strings":["Sorbonne Universit\u00e9 , Observatoire de Paris , Universit\u00e9 PSL , CNRS , LUX , F-75005 Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9 , Observatoire de Paris , Universit\u00e9 PSL , CNRS , LUX , F-75005 Paris , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2746051580","https://openalex.org/I2800004676","https://openalex.org/I39804081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087600868","display_name":"Julien Zylberman","orcid":"https://orcid.org/0000-0002-7785-8246","observed_orcids":["https://orcid.org/0000-0002-7785-8246"]},"institutions":[{"id":"https://openalex.org/I4210106946","display_name":"Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique","ror":"https://ror.org/02dzbc556","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210106946"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Zylberman, Julien","raw_affiliation_strings":["CERFACS , 42 Avenue Gaspard Coriolis , 31057 Toulouse Cedex 1 , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERFACS , 42 Avenue Gaspard Coriolis , 31057 Toulouse Cedex 1 , France","institution_ids":["https://openalex.org/I4210106946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036333287","display_name":"Nuno Loureiro","orcid":"https://orcid.org/0000-0001-9755-6563","observed_orcids":["https://orcid.org/0000-0001-9755-6563"]},"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":"Loureiro, Nuno F.","raw_affiliation_strings":["Plasma Science and Fusion Center , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Plasma Science and Fusion Center , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"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":0.9951000213623047,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.002099999925121665,"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"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-ordinary-differential-equations","display_name":"nonlinear ordinary differential equations","score":0.671999990940094},{"id":"https://openalex.org/keywords/reconstruction-error-bounds","display_name":"reconstruction error bounds","score":0.625},{"id":"https://openalex.org/keywords/amplitude-estimation","display_name":"amplitude estimation","score":0.7799999713897705},{"id":"https://openalex.org/keywords/hadamard-test","display_name":"Hadamard test","score":0.7680000066757202},{"id":"https://openalex.org/keywords/lotka-volterra-model","display_name":"Lotka-Volterra model","score":0.9290000200271606},{"id":"https://openalex.org/keywords/quartic-oscillator","display_name":"quartic oscillator","score":0.9959999918937683},{"id":"https://openalex.org/keywords/conservative-systems","display_name":"conservative systems","score":0.421999990940094}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6869999766349792},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5350000262260437},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4973999857902527},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47620001435279846},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47510001063346863},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.44909998774528503},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4447999894618988},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.42910000681877136},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.36730000376701355},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.36469998955726624},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.36000001430511475},{"id":"https://openalex.org/C103692563","wikidata":"https://www.wikidata.org/wiki/Q5178900","display_name":"Covariance operator","level":3,"score":0.357699990272522},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.329800009727478},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3208000063896179},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.31130000948905945},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.295199990272522},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.29350000619888306},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2913999855518341},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.258899986743927},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.28999","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28999","pdf_url":"https://arxiv.org/pdf/2609.28999","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.2609.28999","doi":"https://doi.org/10.48550/arxiv.2609.28999","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.28999","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:2609.28999","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28999","pdf_url":"https://arxiv.org/pdf/2609.28999","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/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214305672.pdf","grobid_xml":"https://content.openalex.org/works/W7214305672.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1563019883","https://openalex.org/W2415656260","https://openalex.org/W3016493622","https://openalex.org/W4318219738","https://openalex.org/W4367694525","https://openalex.org/W4379516629","https://openalex.org/W4402607687","https://openalex.org/W4404423599","https://openalex.org/W4406160300","https://openalex.org/W4415884649"],"related_works":["https://openalex.org/W4367694525","https://openalex.org/W3111075137","https://openalex.org/W4406160300","https://openalex.org/W4221152681","https://openalex.org/W4389116187","https://openalex.org/W7161834888","https://openalex.org/W7111201286","https://openalex.org/W7212164082","https://openalex.org/W4391244839","https://openalex.org/W4415057911"],"abstract_inverted_index":{"The":[0,79,183,220],"simulation":[1],"of":[2,50,67,93,106,128,158,181,189,233,243],"nonlinear":[3,37,84,108,244],"ordinary":[4,38,245],"differential":[5,39,85,246],"equations":[6,40,86,109],"on":[7,19,41,149,178,186],"quantum":[8,14,43,51,98,190],"computers":[9],"is":[10,60,69,118],"inherently":[11],"challenging,":[12],"as":[13],"gates":[15],"are":[16,87,192],"linear":[17,136],"operators":[18],"qubit":[20],"states.":[21],"In":[22,53],"this":[23,54,111],"paper,":[24],"we":[25],"put":[26],"forth":[27],"a":[28,42,56,63,143,206,241],"Koopman-von":[29],"Neumann":[30],"(KvN)":[31],"operator":[32,73],"based":[33],"algorithm":[34],"for":[35,195,200,229],"solving":[36,107],"computer":[44],"which":[45,68,147],"overcomes":[46],"the":[47,65,76,83,90,103,122,126,129,133,150,156,179,187,196,201,213,217,231,234],"innate":[48],"limitations":[49,105],"operations.":[52],"approach,":[55],"Liouville":[57,112],"probability":[58,237],"density":[59],"embedded":[61],"into":[62],"wavefunction,":[64],"evolution":[66],"governed":[70],"by":[71],"an":[72],"dual":[74],"to":[75,82,125,142,164,172],"Koopman":[77,94],"operator.":[78],"trajectories":[80],"corresponding":[81],"reconstructed":[88],"from":[89,223],"average":[91],"value":[92],"observables":[95],"evaluated":[96],"through":[97],"measurements.":[99],"We":[100,154,204],"specifically":[101],"evaluate":[102],"computational":[104,210],"within":[110],"embedding":[113],"framework.":[114],"An":[115],"Ehrenfest-type":[116],"estimate":[117],"derived":[119],"that":[120],"relates":[121],"reconstruction":[123],"error":[124],"covariance":[127,173],"transported":[130],"density,":[131],"highlighting":[132],"competition":[134],"between":[135],"stretching":[137],"and":[138,169,199],"Hessian-induced":[139],"folding.This":[140],"leads":[141],"key":[144,227],"stability":[145],"criterion,":[146],"depends":[148],"local":[151],"Ehrenfest-Reynolds":[152,214],"number.":[153],"discuss":[155],"effects":[157],"measurement-induced":[159],"errors":[160,211],"including":[161],"those":[162],"due":[163,171],"Hadamard-test":[165],"sampling,":[166],"amplitude":[167],"estimation,":[168],"bias":[170],"in":[174,209],"probabilistic":[175],"Grover-type":[176],"inference":[177],"evaluation":[180],"trajectories.":[182],"limiting":[184],"bounds":[185,221],"accuracy":[188],"computations":[191],"numerically":[193],"verified":[194],"Lotka-Volterra":[197],"system":[198,242],"quartic":[202],"oscillator.":[203],"observe":[205],"rapid":[207],"growth":[208],"when":[212],"number":[215],"approaches":[216],"predicted":[218],"threshold.":[219],"resulting":[222],"our":[224],"analysis":[225],"provide":[226],"guidelines":[228],"selecting":[230],"width":[232],"initial":[235],"Gaussian":[236],"distribution":[238],"associated":[239],"with":[240],"equations.":[247]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}
