{"id":"https://openalex.org/W7134890879","doi":"https://doi.org/10.48550/arxiv.2603.08799","title":"Quantum algorithm for anisotropic diffusion and convection equations with vector norm scaling","display_name":"Quantum algorithm for anisotropic diffusion and convection equations with vector norm scaling","publication_year":2026,"publication_date":"2026-03-09","ids":{"openalex":"https://openalex.org/W7134890879","doi":"https://doi.org/10.48550/arxiv.2603.08799"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.08799","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08799","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.08799","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087600868","display_name":"Julien Zylberman","orcid":"https://orcid.org/0000-0002-7785-8246"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zylberman, Julien","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087286438","display_name":"Thibault Fredon","orcid":"https://orcid.org/0009-0005-9427-9309"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fredon, Thibault","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126481656","display_name":"Nuno F. Loureiro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Loureiro, Nuno F.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5035578344","display_name":"Fabrice Debbasch","orcid":"https://orcid.org/0000-0001-6894-6159"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Debbasch, Fabrice","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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.6154000163078308,"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":0.6154000163078308,"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":0.1177000030875206,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.039799999445676804,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/observable","display_name":"Observable","score":0.5429999828338623},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.44429999589920044},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.44179999828338623},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.42669999599456787},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.41370001435279846},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.39809998869895935},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3774999976158142},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.37459999322891235},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.37229999899864197},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.36959999799728394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5442000031471252},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5429999828338623},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.44429999589920044},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.44179999828338623},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.42669999599456787},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.41370001435279846},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41119998693466187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40139999985694885},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3774999976158142},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.37459999322891235},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.36959999799728394},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.3626999855041504},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.3621000051498413},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.35589998960494995},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.35030001401901245},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C203504353","wikidata":"https://www.wikidata.org/wiki/Q4765461","display_name":"Anisotropic diffusion","level":3,"score":0.3240000009536743},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.31369999051094055},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C157866214","wikidata":"https://www.wikidata.org/wiki/Q17006341","display_name":"Central differencing scheme","level":5,"score":0.2800999879837036},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C2777798563","wikidata":"https://www.wikidata.org/wiki/Q7603916","display_name":"State vector","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.26190000772476196},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.26010000705718994},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2540999948978424}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.08799","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08799","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":"doi:10.48550/arxiv.2603.08799","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08799","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":false,"raw_source_name":null,"raw_type":"article"},"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":{"In":[0],"this":[1],"work,":[2],"we":[3],"tackle":[4],"the":[5,21,26,79,87,93,103,109,115,126],"resolution":[6],"of":[7,37,49,51,82,89,117],"partial":[8],"differential":[9],"equations":[10],"(PDEs)":[11],"on":[12,57],"digital":[13],"quantum":[14,33,40],"computers.":[15],"Two":[16],"fundamental":[17],"PDEs":[18],"are":[19],"addressed:":[20],"anisotropic":[22,27],"diffusion":[23,104],"equation":[24],"and":[25,47,63,106],"convection":[28,110],"equation.":[29],"We":[30,72,84],"present":[31],"a":[32,58,64,99],"numerical":[34],"scheme":[35],"consisting":[36],"three":[38],"steps:":[39],"state":[41],"preparation,":[42],"evolution":[43,54,94],"with":[44],"diagonal":[45],"operators,":[46],"measurement":[48],"observables":[50],"interest.":[52],"The":[53],"step":[55],"relies":[56],"high-order":[59],"centered":[60],"finite":[61],"difference":[62],"product":[65],"formula":[66],"approximation,":[67],"also":[68],"known":[69],"as":[70],"Trotterization.":[71],"provide":[73],"novel":[74],"vector-norm":[75],"analysis":[76],"to":[77,125],"bound":[78],"different":[80],"sources":[81],"error.":[83],"prove":[85],"that":[86],"number":[88,116],"time-steps":[90],"required":[91],"in":[92],"can":[95],"be":[96],"reduced":[97],"by":[98],"factor":[100],"$\u0398(16^n)$":[101],"for":[102,108],"equation,":[105,111],"$\u0398(4^n)$":[107],"where":[112],"$n$":[113],"is":[114],"qubits":[118],"per":[119],"dimension,":[120],"an":[121],"exponential":[122],"reduction":[123],"compared":[124],"previously":[127],"established":[128],"operator-norm":[129],"analysis.":[130]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-12T00:00:00"}
