{"id":"https://openalex.org/W3123862480","doi":"https://doi.org/10.22331/q-2021-11-08-573","title":"On solving classes of positive-definite quantum linear systems with quadratically improved runtime in the condition number","display_name":"On solving classes of positive-definite quantum linear systems with quadratically improved runtime in the condition number","publication_year":2021,"publication_date":"2021-11-08","ids":{"openalex":"https://openalex.org/W3123862480","doi":"https://doi.org/10.22331/q-2021-11-08-573","mag":"3123862480"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-11-08-573","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-11-08-573","pdf_url":"https://quantum-journal.org/papers/q-2021-11-08-573/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-11-08-573/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037442375","display_name":"Davide Orsucci","orcid":"https://orcid.org/0000-0003-3087-8757"},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Davide Orsucci","raw_affiliation_strings":["Institut f\u00fcr Kommunikation und Navigation, Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), M\u00fcnchener Str. 20, 82234 We\u00dfling, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Kommunikation und Navigation, Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), M\u00fcnchener Str. 20, 82234 We\u00dfling, Germany","institution_ids":["https://openalex.org/I2898391981"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069043772","display_name":"Vedran Dunjko","orcid":"https://orcid.org/0000-0002-2632-7955"},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Vedran Dunjko","raw_affiliation_strings":["Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037442375"],"corresponding_institution_ids":["https://openalex.org/I2898391981"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.2799,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61304016,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":null,"first_page":"573","last_page":"573"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"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":0.9998999834060669,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9977999925613403,"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":0.9948999881744385,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.6918363571166992},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5963619947433472},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.5884508490562439},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48059818148612976},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4769912362098694},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4435168504714966},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43962353467941284},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.43913936614990234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4384717047214508},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41522833704948425},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.41381925344467163},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37154024839401245},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3505527377128601},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3479887843132019},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14672908186912537},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09061405062675476},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08259791135787964},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07822751998901367}],"concepts":[{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.6918363571166992},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5963619947433472},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.5884508490562439},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48059818148612976},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4769912362098694},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4435168504714966},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43962353467941284},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.43913936614990234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4384717047214508},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41522833704948425},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.41381925344467163},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37154024839401245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3505527377128601},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3479887843132019},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14672908186912537},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09061405062675476},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08259791135787964},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07822751998901367},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.22331/q-2021-11-08-573","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-11-08-573","pdf_url":"https://quantum-journal.org/papers/q-2021-11-08-573/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:elib.dlr.de:145449","is_oa":false,"landing_page_url":"https://doi.org/10.22331/q-2021-11-08-573>.","pdf_url":null,"source":{"id":"https://openalex.org/S4377196266","display_name":"elib (German Aerospace Center)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2898391981","host_organization_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","host_organization_lineage":["https://openalex.org/I2898391981"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"mag:3123862480","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2101.11868.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:6a00a8e6873b490a9b117df26c85838e","is_oa":true,"landing_page_url":"https://doaj.org/article/6a00a8e6873b490a9b117df26c85838e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 5, p 573 (2021)","raw_type":"article"},{"id":"pmh:oai:scholarlypublications.universiteitleiden.nl:item_3277184","is_oa":true,"landing_page_url":"https://hdl.handle.net/1887/3277184","pdf_url":null,"source":{"id":"https://openalex.org/S4306400850","display_name":"Leiden Repository (Leiden University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I121797337","host_organization_name":"Leiden University","host_organization_lineage":["https://openalex.org/I121797337"],"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":"Quantum","raw_type":"Article / Letter to editor"},{"id":"pmh:ul:oai:scholarlypublications.universiteitleiden.nl:item_3277184","is_oa":true,"landing_page_url":"http://hdl.handle.net/1887/3277184","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"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":"Quantum, 5, 573. VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2101.11868","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2101.11868","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-journal"}],"best_oa_location":{"id":"doi:10.22331/q-2021-11-08-573","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-11-08-573","pdf_url":"https://quantum-journal.org/papers/q-2021-11-08-573/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1211560647","display_name":null,"funder_award_id":"24.003.037","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G249262831","display_name":null,"funder_award_id":"024.003.037","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G420050720","display_name":null,"funder_award_id":"024.003","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4418824033","display_name":null,"funder_award_id":"024.003.03","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4499217744","display_name":null,"funder_award_id":"NWO/OCW","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3123862480.pdf","grobid_xml":"https://content.openalex.org/works/W3123862480.grobid-xml"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W1492999010","https://openalex.org/W1506342804","https://openalex.org/W1527197079","https://openalex.org/W1624621931","https://openalex.org/W1631356911","https://openalex.org/W1979112316","https://openalex.org/W2020918964","https://openalex.org/W2029029634","https://openalex.org/W2041506125","https://openalex.org/W2041606052","https://openalex.org/W2042127289","https://openalex.org/W2051446825","https://openalex.org/W2059998776","https://openalex.org/W2080855151","https://openalex.org/W2096334625","https://openalex.org/W2097174474","https://openalex.org/W2098246547","https://openalex.org/W2098841537","https://openalex.org/W2104590612","https://openalex.org/W2121981260","https://openalex.org/W2144267444","https://openalex.org/W2183393041","https://openalex.org/W2208142350","https://openalex.org/W2332701672","https://openalex.org/W2415656260","https://openalex.org/W2432517183","https://openalex.org/W2535738892","https://openalex.org/W2607911764","https://openalex.org/W2734667871","https://openalex.org/W2761673598","https://openalex.org/W2792324887","https://openalex.org/W2795534239","https://openalex.org/W2804737001","https://openalex.org/W2805612073","https://openalex.org/W2806751077","https://openalex.org/W2813120584","https://openalex.org/W2862348988","https://openalex.org/W2902420940","https://openalex.org/W2963479547","https://openalex.org/W2963652075","https://openalex.org/W3002693700","https://openalex.org/W3007060332","https://openalex.org/W3010344614","https://openalex.org/W3032861285","https://openalex.org/W3082879362","https://openalex.org/W3083786773","https://openalex.org/W3087818863","https://openalex.org/W3098858679","https://openalex.org/W3100122058","https://openalex.org/W3101249570","https://openalex.org/W3101824094","https://openalex.org/W3104433882","https://openalex.org/W3104890289","https://openalex.org/W3105421460","https://openalex.org/W3106123690","https://openalex.org/W3113189095","https://openalex.org/W3124690791","https://openalex.org/W3145116593","https://openalex.org/W3217033513","https://openalex.org/W4213408129","https://openalex.org/W4254246953","https://openalex.org/W4298227433","https://openalex.org/W6600585467","https://openalex.org/W6604965747","https://openalex.org/W6677055984"],"related_works":["https://openalex.org/W3213578166","https://openalex.org/W2207541471","https://openalex.org/W2895607801","https://openalex.org/W2948580656","https://openalex.org/W2910080157","https://openalex.org/W2119985177","https://openalex.org/W2518339813","https://openalex.org/W2787200178","https://openalex.org/W1504306194","https://openalex.org/W2141276839","https://openalex.org/W2136256176","https://openalex.org/W2297342589","https://openalex.org/W1605113654","https://openalex.org/W2950918963","https://openalex.org/W1996669750","https://openalex.org/W2997085175","https://openalex.org/W2975402360","https://openalex.org/W2962705227","https://openalex.org/W2408897693","https://openalex.org/W3005680708"],"abstract_inverted_index":{"Quantum":[0,5],"algorithms":[1,16,98,182],"for":[2,70,91],"solving":[3,145],"the":[4,12,24,40,48,52,63,66,73,92,115,116,138,141,190,203,209,215],"Linear":[6],"System":[7],"(QLS)":[8],"problem":[9,68],"are":[10,219],"among":[11],"most":[13],"investigated":[14],"quantum":[15,181],"of":[17,26,42,51,65,94,167,199,208],"recent":[18],"times,":[19],"with":[20,103],"potential":[21],"applications":[22],"including":[23],"solution":[25],"computationally":[27],"intractable":[28],"differential":[29],"equations":[30],"and":[31,84,177,222],"speed-ups":[32],"in":[33,79,140,152,187],"machine":[34],"learning.":[35],"A":[36],"fundamental":[37],"parameter":[38],"governing":[39],"efficiency":[41],"QLS":[43,67,126,147,169],"solvers":[44,127],"is":[45,120,159,192],"<mml:math":[46,55,80,108,153,157,188,200,211],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03ba</mml:mi></mml:math>,":[47],"condition":[49],"number":[50],"coefficient":[53],"matrix":[54],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>A</mml:mi></mml:math>,":[56],"as":[57,107],"it":[58],"has":[59],"been":[60],"known":[61],"since":[62],"inception":[64],"that":[69,144],"worst-case":[71],"instances":[72],"runtime":[74,105,150],"scales":[75],"at":[76],"least":[77],"linearly":[78],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03ba</mml:mi></mml:math>":[81,154],"[Harrow,":[82],"Hassidim":[83],"Lloyd,":[85],"PRL":[86],"103,":[87],"150502":[88],"(2009)].":[89],"However,":[90],"case":[93],"positive-definite":[95,168],"matrices":[96],"classical":[97],"can":[99,174],"solve":[100,227],"linear":[101,151],"systems":[102],"a":[104,110,146,149,184,197,206],"scaling":[106],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msqrt><mml:mi>\u03ba</mml:mi></mml:msqrt></mml:math>,":[109],"quadratic":[111,185],"improvement":[112],"compared":[113],"to":[114,123,213,225],"indefinite":[117],"case.":[118],"It":[119],"then":[121,163],"natural":[122],"ask":[124],"whether":[125],"may":[128],"hold":[129],"an":[130],"analogous":[131],"improvement.":[132],"In":[133],"this":[134,171],"work":[135],"we":[136],"answer":[137],"question":[139],"negative,":[142],"showing":[143],"entails":[148],"also":[155],"when":[156],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>A</mml:mi></mml:math>":[158],"positive":[160],"definite.":[161],"We":[162],"identify":[164],"broad":[165],"classes":[166],"where":[170],"lower":[172],"bound":[173],"be":[175],"circumvented":[176],"present":[178],"two":[179],"new":[180],"featuring":[183],"speed-up":[186],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03ba</mml:mi></mml:math>:":[189],"first":[191],"based":[193],"on":[194],"efficiently":[195,226],"implementing":[196],"matrix-block-encoding":[198],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>A</mml:mi><mml:mrow":[201],"class=\"MJX-TeXAtom-ORD\"><mml:mo>\u2212</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>,":[202],"second":[204],"constructs":[205],"decomposition":[207],"form":[210],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:msup><mml:mi>L</mml:mi><mml:mo>\u2020</mml:mo></mml:msup></mml:math>":[212],"precondition":[214],"system.":[216],"These":[217],"methods":[218],"widely":[220],"applicable":[221],"both":[223],"allow":[224],"BQP-complete":[228],"problems.":[229]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}