{"id":"https://openalex.org/W7220919645","doi":"https://doi.org/10.48550/arxiv.2610.06987","title":"A structure-aware construction of quantum BPX preconditioners for Q1 finite element discretizations of reaction-diffusion problems","display_name":"A structure-aware construction of quantum BPX preconditioners for Q1 finite element discretizations of reaction-diffusion problems","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220919645","doi":"https://doi.org/10.48550/arxiv.2610.06987"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06987","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06987","pdf_url":"https://arxiv.org/pdf/2610.06987","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/2610.06987","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157931987","display_name":"Yin Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang, Yin","raw_affiliation_strings":["School of Mathematics and Computational Science , Xiangtan University , Xiangtan , Hunan 411105 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science , Xiangtan University , Xiangtan , Hunan 411105 , China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157975761","display_name":"Yue Yu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu, Yue","raw_affiliation_strings":["Hunan Research Center of the Basic Discipline Fundamental Algorithmic Theory and Novel Computational Methods , Xiangtan , Hunan 411105 , China National Center for Applied Mathematics in Hunan , Xiangtan , Hunan 411105 , China","School of Mathematics and Computational Science , Xiangtan University , Xiangtan , Hunan 411105 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Research Center of the Basic Discipline Fundamental Algorithmic Theory and Novel Computational Methods , Xiangtan , Hunan 411105 , China National Center for Applied Mathematics in Hunan , Xiangtan , Hunan 411105 , China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"School of Mathematics and Computational Science , Xiangtan University , Xiangtan , Hunan 411105 , China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157972999","display_name":"Long Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Long","raw_affiliation_strings":["School of Mathematics and Computational Science , Xiangtan University , Xiangtan , Hunan 411105 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science , Xiangtan University , Xiangtan , Hunan 411105 , China","institution_ids":["https://openalex.org/I4610292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4610292"],"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":0.9839000105857849,"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":0.9839000105857849,"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":0.004600000102072954,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.002899999963119626,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bpx-preconditioner","display_name":"BPX preconditioner","score":0.8040000200271606},{"id":"https://openalex.org/keywords/multilevel-preconditioners","display_name":"multilevel preconditioning","score":0.8159999847412109},{"id":"https://openalex.org/keywords/reaction-diffusion-systems","display_name":"reaction-diffusion systems","score":0.9409999847412109},{"id":"https://openalex.org/keywords/poisson-equation","display_name":"Poisson equation","score":0.9850000143051147},{"id":"https://openalex.org/keywords/linear-quantum-systems","display_name":"quantum linear systems","score":0.6449999809265137},{"id":"https://openalex.org/keywords/query-complexity","display_name":"query complexity","score":0.8059999942779541}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.8173999786376953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7044000029563904},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6665999889373779},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5774000287055969},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4465000033378601},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4438999891281128},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44359999895095825},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.38100001215934753},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.3772999942302704},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3580000102519989},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.35409998893737793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.353300005197525},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.311599999666214},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3041999936103821},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.29679998755455017},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.29409998655319214},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.2840999960899353}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06987","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06987","pdf_url":"https://arxiv.org/pdf/2610.06987","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.2610.06987","doi":"https://doi.org/10.48550/arxiv.2610.06987","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06987","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.06987","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06987","pdf_url":"https://arxiv.org/pdf/2610.06987","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/G2177410009","display_name":null,"funder_award_id":"2024JC1003","funder_id":"https://openalex.org/F4320321471","funder_display_name":"Hunan Provincial Science and Technology Department"},{"id":"https://openalex.org/G2398811793","display_name":null,"funder_award_id":"2024JJ1008","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G2617215043","display_name":null,"funder_award_id":"12341104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3896635305","display_name":null,"funder_award_id":"SRICSPYF-BS2025132","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4659690726","display_name":null,"funder_award_id":"2024JC1003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4934396703","display_name":null,"funder_award_id":"2024JC1003","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G627238494","display_name":null,"funder_award_id":"2024JJ1008","funder_id":"https://openalex.org/F4320321471","funder_display_name":"Hunan Provincial Science and Technology Department"},{"id":"https://openalex.org/G650865851","display_name":null,"funder_award_id":"12301561","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8081541980","display_name":null,"funder_award_id":"D23017","funder_id":"https://openalex.org/F4320335801","funder_display_name":"Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province"},{"id":"https://openalex.org/G8351604488","display_name":null,"funder_award_id":"12571469","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8418242333","display_name":null,"funder_award_id":"D23017","funder_id":"https://openalex.org/F4320327912","funder_display_name":"Higher Education Discipline Innovation Project"},{"id":"https://openalex.org/G8944349641","display_name":"\u5206\u6570\u9636\u5fae\u5206\u65b9\u7a0b\u7684\u91cf\u5b50\u7b97\u6cd5\u7814\u7a76","funder_award_id":"2026JJ50003","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321471","display_name":"Hunan Provincial Science and Technology Department","ror":"https://ror.org/04qgr7x96"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320324780","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62"},{"id":"https://openalex.org/F4320327912","display_name":"Higher Education Discipline Innovation Project","ror":null},{"id":"https://openalex.org/F4320335801","display_name":"Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220919645.pdf","grobid_xml":"https://content.openalex.org/works/W7220919645.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2805612073"],"related_works":["https://openalex.org/W7162397930","https://openalex.org/W7128246374","https://openalex.org/W4413073100","https://openalex.org/W2244594781","https://openalex.org/W7097533069","https://openalex.org/W2528707554","https://openalex.org/W1970651303","https://openalex.org/W2068135461","https://openalex.org/W282614906","https://openalex.org/W7110910808"],"abstract_inverted_index":{"We":[0,76,173],"present":[1],"a":[2,67,119,187],"structure-aware":[3],"construction":[4,85,181],"of":[5,14,66,90],"quantum":[6,29],"BPX":[7],"preconditioners":[8],"for":[9,153,160,169],"Q1":[10],"finite":[11,30,33,72,93],"element":[12,31,73,94],"discretizations":[13],"constant-coefficient":[15],"reaction--diffusion":[16],"equations":[17],"on":[18,27,166],"the":[19,23,38,70,79,84,87,91,100,108,138,143,148,180],"unit":[20],"cube,":[21],"including":[22],"Poisson":[24],"equation.":[25],"Building":[26],"existing":[28],"and":[32,47,56,151,162,178,182],"difference":[34],"methods,":[35],"we":[36,112],"express":[37],"preconditioned":[39,109],"operator":[40],"through":[41],"explicit":[42],"one-dimensional":[43,188],"maps,":[44],"tensor":[45],"products,":[46],"norm-preserving":[48],"interlevel":[49],"transfers.":[50],"Symmetric":[51],"preconditioning":[52],"gives":[53],"multilevel":[54],"coefficients,":[55],"its":[57],"favorable":[58],"conditioning":[59],"alone":[60],"does":[61],"not":[62],"ensure":[63],"efficient":[64],"recovery":[65],"state":[68,117],"in":[69],"original":[71],"nodal":[74],"basis.":[75],"instead":[77],"use":[78],"local":[80],"$L^2$-orthonormal":[81],"basis":[82],"underlying":[83],"as":[86],"output":[88],"representation":[89],"same":[92],"function.":[95],"Its":[96],"coefficient":[97,116],"norm":[98],"equals":[99],"continuous":[101,171,183],"$L^2$":[102],"norm.":[103],"Assuming":[104],"direct":[105],"access":[106],"to":[107],"right-hand":[110,144],"side,":[111,145],"prepare":[113],"this":[114],"orthonormal":[115],"with":[118,186],"represented":[120],"function":[121],"error":[122,184],"at":[123],"most":[124],"$\\varepsilon$.":[125],"The":[126,157],"expected":[127],"query":[128],"complexity":[129],"is":[130,137,142,147],"\\[":[131],"\\mathcal{O}\\!\\Big(dL^3\\frac{\\|f\\|_{L^2}}{\\|u\\|_{L^2}}":[132],"\\log\\!\\Big(2+\\frac{L\\|f\\|_{L^2}}{\\varepsilon}\\Big)\\Big),":[133],"\\]":[134],"where":[135],"$u$":[136],"exact":[139],"solution,":[140],"$f$":[141],"$d$":[146],"spatial":[149],"dimension,":[150],"$L=\\log_2(1/h)$":[152],"mesh":[154,167],"width":[155],"$h$.":[156],"bound":[158],"holds":[159],"$0<\\varepsilon\\le\\|u\\|_{L^2}/2$":[161],"depends":[163],"only":[164],"polylogarithmically":[165],"refinement":[168],"fixed":[170],"data.":[172],"also":[174],"analyze":[175],"linear-functional":[176],"estimation":[177],"illustrate":[179],"bounds":[185],"UnitaryLab":[189],"experiment.":[190]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}