{"id":"https://openalex.org/W7162397930","doi":"https://doi.org/10.48550/arxiv.2605.26090","title":"Quantum Domain Decomposition for Preconditioning the Finite Element Method","display_name":"Quantum Domain Decomposition for Preconditioning the Finite Element Method","publication_year":2026,"publication_date":"2026-05-25","ids":{"openalex":"https://openalex.org/W7162397930","doi":"https://doi.org/10.48550/arxiv.2605.26090"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.26090","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26090","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2605.26090","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007556861","display_name":"\u00c9lise Fressart","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fressart, Elise","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111420160","display_name":"Michel Nowak","orcid":"https://orcid.org/0000-0002-3016-0844"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nowak, Michel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076520272","display_name":"Nicole Spillane","orcid":"https://orcid.org/0000-0001-5067-946X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Spillane, Nicole","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.8263000249862671,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.8263000249862671,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.048500001430511475,"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/T12303","display_name":"Tensor decomposition and applications","score":0.020099999383091927,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/preconditioner","display_name":"Preconditioner","score":0.9200000166893005},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.8046000003814697},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.6340000033378601},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.560699999332428},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5291000008583069},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5153999924659729},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.513700008392334},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.508400022983551},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5001000165939331}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9200000166893005},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.8046000003814697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6990000009536743},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.6340000033378601},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.560699999332428},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5153999924659729},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.513700008392334},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.508400022983551},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5001000165939331},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4986000061035156},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.48820000886917114},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46239998936653137},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.41370001435279846},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3896999955177307},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.34439998865127563},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C97110765","wikidata":"https://www.wikidata.org/wiki/Q17099078","display_name":"Mortar methods","level":4,"score":0.30809998512268066},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30630001425743103},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29809999465942383},{"id":"https://openalex.org/C192465680","wikidata":"https://www.wikidata.org/wiki/Q1413450","display_name":"Precondition","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.2734000086784363},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.26899999380111694},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.2669999897480011},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.25999999046325684}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.26090","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26090","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.26090","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26090","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"Even":[0],"in":[1,66],"cases":[2],"where":[3],"quantum":[4,107,153],"linear":[5,53,154],"solvers":[6],"provide":[7,111,190],"significant":[8],"speedup":[9],"compared":[10],"to":[11,34,50,105],"their":[12,15],"classical":[13],"counterparts,":[14],"performance":[16],"depends":[17],"on":[18,90,160,183,192],"some":[19],"of":[20,29,74,83,93,118,137,151,164],"the":[21,26,30,52,71,80,115,119,124,131,138,149,152,168,184,194],"same":[22],"parameters.":[23],"In":[24,85],"particular,":[25],"condition":[27,72,81],"number":[28,73,82],"matrix":[31,64],"which":[32],"is":[33,37,49,76,103],"be":[35],"inverted":[36],"a":[38,63,68,91,161],"decisive":[39],"parameter.":[40],"A":[41],"well":[42],"known":[43],"classical,":[44],"and":[45,128,178],"now":[46],"quantum,":[47],"remedy":[48],"precondition":[51],"system":[54,155],"$A":[55],"x":[56],"=":[57],"b$":[58],"by":[59,62,123,130,172,176],"premultiplying":[60],"it":[61,102],"$H$":[65],"such":[67],"way":[69],"that":[70,101],"$HA$":[75],"significantly":[77],"smaller":[78],"than":[79],"$A$.":[84],"this":[86],"work,":[87],"we":[88,99,147,158,189],"focus":[89,159],"family":[92],"preconditioners":[94],"called":[95],"domain":[96,108,141,169],"decomposition.":[97,109],"First,":[98],"prove":[100],"feasible":[104],"apply":[106],"We":[110],"upper":[112],"bounds":[113],"for":[114],"block-encoding":[116],"parameters":[117],"Poisson":[120],"problem":[121],"discretized":[122],"finite":[125],"element":[126],"method":[127],"preconditioned":[129],"two-level":[132],"Additive":[133],"Schwarz":[134],"preconditioner":[135,171],"(one":[136],"most":[139],"fundamental":[140],"decomposition":[142,170],"techniques).":[143],"From":[144],"these":[145],"bounds,":[146],"deduce":[148],"complexity":[150],"solver.":[156],"Second,":[157],"particular":[162],"choice":[163],"local":[165],"solver":[166],"within":[167],"applying":[173],"recent":[174],"work":[175],"[Deiml":[177],"Peterseim,":[179],"\\textit{Math.":[180],"Comput.},":[181],"2025]":[182],"Bramble--Pasciak--Xu":[185],"(BPX)":[186],"preconditioner.":[187],"Finally,":[188],"details":[191],"how":[193],"operators":[195],"are":[196],"implemented.":[197]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-27T00:00:00"}
