{"id":"https://openalex.org/W4416912862","doi":"https://doi.org/10.1137/25m1761513","title":"An Implementation of Quantum Oracles for the Finite Element Method","display_name":"An Implementation of Quantum Oracles for the Finite Element Method","publication_year":2026,"publication_date":"2026-06-01","ids":{"openalex":"https://openalex.org/W4416912862","doi":"https://doi.org/10.1137/25m1761513"},"language":"en","primary_location":{"id":"doi:10.1137/25m1761513","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1761513","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2504.19827","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087783751","display_name":"Sven Danz","orcid":"https://orcid.org/0009-0008-5083-3920"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sven Danz","raw_affiliation_strings":["Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany, and Theoretical Physics, Saarland University, 66123, Saarbr\u00fccken, Germany"],"raw_orcid":"https://orcid.org/0009-0008-5083-3920","affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany, and Theoretical Physics, Saarland University, 66123, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090753886","display_name":"Tobias Stollenwerk","orcid":"https://orcid.org/0000-0001-5445-8082"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias Stollenwerk","raw_affiliation_strings":["Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026482786","display_name":"Alessandro Ciani","orcid":"https://orcid.org/0000-0002-8707-0532"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alessandro Ciani","raw_affiliation_strings":["Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum J\u00fclich, 52425 J\u00fclich, Germany","institution_ids":["https://openalex.org/I171892758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I171892758"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01877549,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"3","first_page":"B386","last_page":"B419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.839900016784668,"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":0.839900016784668,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.020500000566244125,"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/T11416","display_name":"Numerical methods for differential equations","score":0.014700000174343586,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subroutine","display_name":"Subroutine","score":0.694100022315979},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.6657999753952026},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5813999772071838},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5774999856948853},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5751000046730042},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.5062000155448914},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.48089998960494995},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4677000045776367},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.453000009059906}],"concepts":[{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.694100022315979},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.6657999753952026},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5813999772071838},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5774999856948853},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5751000046730042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5468000173568726},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5062000155448914},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.48089998960494995},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4677000045776367},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.453000009059906},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.4447999894618988},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42559999227523804},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.40880000591278076},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3955000042915344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3952000141143799},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3668999969959259},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3476000130176544},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3400000035762787},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.33079999685287476},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.329800009727478},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.28690001368522644},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.26440000534057617},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.2538999915122986}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/25m1761513","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1761513","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:juser.fz-juelich.de:1052609","is_oa":false,"landing_page_url":"https://juser.fz-juelich.de/record/1052609","pdf_url":null,"source":{"id":"https://openalex.org/S4306401090","display_name":"JuSER (Forschungszentrum J\u00fclich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I171892758","host_organization_name":"Forschungszentrum J\u00fclich","host_organization_lineage":["https://openalex.org/I171892758"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"arXiv (2025). doi:10.48550/ARXIV.2504.19827","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2504.19827","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.19827","pdf_url":"https://arxiv.org/pdf/2504.19827","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:arXiv.org:2504.19827","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2504.19827","pdf_url":"https://arxiv.org/pdf/2504.19827","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2504.19827","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2504.19827","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2504.19827","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.19827","pdf_url":"https://arxiv.org/pdf/2504.19827","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7244240807","display_name":null,"funder_award_id":"01MQ22001A","funder_id":"https://openalex.org/F4303701741","funder_display_name":"Bundesministerium f\u00fcr Wirtschaft und Klimaschutz"}],"funders":[{"id":"https://openalex.org/F4303701741","display_name":"Bundesministerium f\u00fcr Wirtschaft und Klimaschutz","ror":"https://ror.org/02vgg2808"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416912862.pdf","grobid_xml":"https://content.openalex.org/works/W4416912862.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W2084213553","https://openalex.org/W2102008187","https://openalex.org/W2101903351","https://openalex.org/W2061073612","https://openalex.org/W4392662757","https://openalex.org/W2098948451","https://openalex.org/W2041506125","https://openalex.org/W4396945043","https://openalex.org/W2050334794","https://openalex.org/W2148132004","https://openalex.org/W2463283279","https://openalex.org/W1601728065","https://openalex.org/W2500415654","https://openalex.org/W2118495140","https://openalex.org/W4295960356","https://openalex.org/W3138121209","https://openalex.org/W2759506558","https://openalex.org/W2805612073","https://openalex.org/W2084652510","https://openalex.org/W2085795790","https://openalex.org/W45896552","https://openalex.org/W2964211946","https://openalex.org/W2415656260","https://openalex.org/W2535738892","https://openalex.org/W4200164985","https://openalex.org/W2208142350","https://openalex.org/W2972575096","https://openalex.org/W4307641337","https://openalex.org/W1992000520","https://openalex.org/W4395082345","https://openalex.org/W1503961870","https://openalex.org/W3023478445","https://openalex.org/W2962908530","https://openalex.org/W1563668274","https://openalex.org/W2017278808","https://openalex.org/W2035112473"],"related_works":[],"abstract_inverted_index":{"In":[0],"order":[1,132],"to":[2,72,162],"assess":[3],"potential":[4,204],"advantages":[5,208],"of":[6,18,22,38,44,61,81,88,142,159,189],"quantum":[7,11,32,67,93],"algorithms":[8],"that":[9,182,193],"require":[10,78],"oracles":[12,24,39],"as":[13,175],"subroutines,":[14],"the":[15,19,23,31,36,42,45,57,74,79,86,105,131,137,140,145,149,157,164,167,183,194],"careful":[16],"evaluation":[17],"overall":[20],"complexity":[21],"themselves":[25],"is":[26],"crucial.":[27],"This":[28],"study":[29],"examines":[30],"routines":[33],"required":[34],"for":[35,148],"implementation":[37,87],"used":[40,161],"in":[41,56,144,171,199,209],"block-encoding":[43],"$N":[46],"\\times":[47],"N$":[48],"stiffness":[49],"and":[50,85,118,154,166,180],"mass":[51],"matrices,":[52],"which":[53,77,134],"typically":[54],"emerge":[55],"finite":[58],"element":[59],"analysis":[60],"elastic":[62],"structures.":[63],"Starting":[64],"from":[65],"basic":[66],"adders,":[68],"we":[69,135],"show":[70],"how":[71],"construct":[73,104],"necessary":[75],"oracles,":[76,195],"calculation":[80],"polynomials,":[82,138],"square":[83,150],"root":[84],"conditional":[89],"operations.":[90],"We":[91],"propose":[92],"subroutines":[94],"based":[95],"on":[96],"fixed-point":[97],"arithmetic":[98],"that,":[99],"given":[100],"an":[101],"$r$-qubit":[102],"register,":[103],"oracle":[106],"using":[107],"$\\mathcal{O}((K":[108,121],"+":[109,111,113,122,124,126],"L":[110],"N_{\\mathrm{geo}}":[112],"N_{\\mathrm{D}})":[114],"r)$":[115],"ancilla":[116],"qubits":[117],"have":[119],"a":[120],"L)r^2":[123],"\\log_2(N_{\\mathrm{geo}}":[125],"N_{\\mathrm{D}}))$":[127],"runtime,":[128],"with":[129],"$K$":[130],"at":[133],"truncate":[136],"$L$":[139],"number":[141,158],"iterations":[143],"Newton-Raphson":[146],"subroutine":[147],"root,":[151],"while":[152,196],"$N_{\\mathrm{geo}}$":[153],"$N_{\\mathrm{D}}$":[155],"are":[156,186],"hypercuboids":[160],"approximate":[163],"geometry":[165],"boundary,":[168],"respectively.":[169],"Since":[170],"practice":[172],"$r$":[173],"scales":[174],"$r":[176],"=":[177],"\\mathcal{O}(\\log_2":[178],"N)$,":[179],"assuming":[181],"other":[184],"parameters":[185],"fixed":[187],"independently":[188],"$N$,":[190],"this":[191],"shows":[192],"still":[197],"costly":[198],"practice,":[200],"do":[201],"not":[202],"endanger":[203],"polynomial":[205],"or":[206],"exponential":[207],"$N$.":[210]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
