{"id":"https://openalex.org/W3098858679","doi":"https://doi.org/10.22331/q-2020-11-11-361","title":"Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems","display_name":"Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems","publication_year":2020,"publication_date":"2020-11-11","ids":{"openalex":"https://openalex.org/W3098858679","doi":"https://doi.org/10.22331/q-2020-11-11-361","mag":"3098858679"},"language":"en","primary_location":{"id":"doi:10.22331/q-2020-11-11-361","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-11-11-361","pdf_url":"https://quantum-journal.org/papers/q-2020-11-11-361/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":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2020-11-11-361/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Lin Lin","orcid":"https://orcid.org/0000-0001-6860-9566"},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Lin Lin","raw_affiliation_strings":["Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA","Department of Mathematics, University of California, Berkeley, CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I148283060"]},{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":null,"display_name":"Yu Tong","orcid":"https://orcid.org/0000-0002-7555-9373"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu Tong","raw_affiliation_strings":["Department of Mathematics, University of California, Berkeley, CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I148283060","https://openalex.org/I95457486"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":5.5727,"has_fulltext":true,"cited_by_count":96,"citation_normalized_percentile":{"value":0.9664288,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"4","issue":null,"first_page":"361","last_page":"361"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.8830999732017517,"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":0.8830999732017517,"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":0.09120000153779984,"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/T11177","display_name":"Spectroscopy and Quantum Chemical Studies","score":0.0026000000070780516,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/quantum-phase-estimation-algorithm","display_name":"Quantum phase estimation algorithm","score":0.7031000256538391},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.6366999745368958},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5972999930381775},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5091000199317932},{"id":"https://openalex.org/keywords/quantum-algorithm-for-linear-systems-of-equations","display_name":"Quantum algorithm for linear systems of equations","score":0.5054000020027161},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.4810999929904938},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.4505999982357025},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43560001254081726},{"id":"https://openalex.org/keywords/quantum-fourier-transform","display_name":"Quantum Fourier transform","score":0.42579999566078186}],"concepts":[{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.7031000256538391},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.6366999745368958},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5972999930381775},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.564300000667572},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5091000199317932},{"id":"https://openalex.org/C101471828","wikidata":"https://www.wikidata.org/wiki/Q17083575","display_name":"Quantum algorithm for linear systems of equations","level":5,"score":0.5054000020027161},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4810999929904938},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45500001311302185},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.4505999982357025},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.42579999566078186},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.41780000925064087},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.39320001006126404},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.39089998602867126},{"id":"https://openalex.org/C109663097","wikidata":"https://www.wikidata.org/wiki/Q182453","display_name":"Adiabatic process","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C192353077","wikidata":"https://www.wikidata.org/wiki/Q4682635","display_name":"Adiabatic quantum computation","level":4,"score":0.3580999970436096},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.35519999265670776},{"id":"https://openalex.org/C194867977","wikidata":"https://www.wikidata.org/wiki/Q1897309","display_name":"Quantum Zeno effect","level":4,"score":0.35019999742507935},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.3190000057220459},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.31630000472068787},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.301800012588501},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2924000024795532},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C191608238","wikidata":"https://www.wikidata.org/wiki/Q5249552","display_name":"Decoherence-free subspaces","level":5,"score":0.25279998779296875}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2020-11-11-361","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-11-11-361","pdf_url":"https://quantum-journal.org/papers/q-2020-11-11-361/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:arXiv.org:1910.14596","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.14596","pdf_url":"https://arxiv.org/pdf/1910.14596","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":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:99ffe2843a1c43cc882088d424fe1ae9","is_oa":true,"landing_page_url":"https://doaj.org/article/99ffe2843a1c43cc882088d424fe1ae9","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 4, p 361 (2020)","raw_type":"article"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt0z44w3z1","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/0z44w3z1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"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":"article"},{"id":"pmh:oai:osti.gov:1763676","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1763676","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"doi:10.22331/q-2020-11-11-361","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-11-11-361","pdf_url":"https://quantum-journal.org/papers/q-2020-11-11-361/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/G1065316766","display_name":null,"funder_award_id":"Award","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G1286236842","display_name":null,"funder_award_id":"-AC02-05CH11231","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2978463324","display_name":null,"funder_award_id":"FA9550-18-1-00","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3083819904","display_name":null,"funder_award_id":"05CH11231","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3310577945","display_name":null,"funder_award_id":"DE-AC02-05CH11231","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G425189044","display_name":null,"funder_award_id":"DE-AC02-05CH","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5238257719","display_name":null,"funder_award_id":"DE-SC0017867","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5315912995","display_name":null,"funder_award_id":"11231","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6330738325","display_name":null,"funder_award_id":"DE_AC02_05CH11231","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6348972864","display_name":null,"funder_award_id":"AC02-05CH11231","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6429026066","display_name":null,"funder_award_id":"DE-AC02-05CH112","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6558272803","display_name":null,"funder_award_id":"DE-AC02","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7320122463","display_name":null,"funder_award_id":"FA9550-18-1-0095","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7340683655","display_name":null,"funder_award_id":"E-AC02-05CH11231","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7406122311","display_name":null,"funder_award_id":"AC02-05CH1123","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7825954517","display_name":null,"funder_award_id":"DE-AC02-05CH1123","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7970117537","display_name":null,"funder_award_id":"FA9550-18-1-0095","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G8414908677","display_name":null,"funder_award_id":"DE-AC0","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G969889393","display_name":null,"funder_award_id":"DE-AC02-","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3098858679.pdf","grobid_xml":"https://content.openalex.org/works/W3098858679.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1561344775","https://openalex.org/W1578898693","https://openalex.org/W1871899311","https://openalex.org/W1989383224","https://openalex.org/W1993252541","https://openalex.org/W1997391728","https://openalex.org/W2013879218","https://openalex.org/W2016230469","https://openalex.org/W2037354050","https://openalex.org/W2040792108","https://openalex.org/W2064769982","https://openalex.org/W2078860479","https://openalex.org/W2079656262","https://openalex.org/W2079692740","https://openalex.org/W2080919950","https://openalex.org/W2082404199","https://openalex.org/W2084652510","https://openalex.org/W2089974384","https://openalex.org/W2094329495","https://openalex.org/W2096334625","https://openalex.org/W2097174474","https://openalex.org/W2105472443","https://openalex.org/W2121981260","https://openalex.org/W2144456193","https://openalex.org/W2151365767","https://openalex.org/W2415656260","https://openalex.org/W2535738892","https://openalex.org/W2564229214","https://openalex.org/W2607911764","https://openalex.org/W2761673598","https://openalex.org/W2766294686","https://openalex.org/W2775563604","https://openalex.org/W2791899439","https://openalex.org/W2793302002","https://openalex.org/W2795534239","https://openalex.org/W2805612073","https://openalex.org/W2809863118","https://openalex.org/W2880299821","https://openalex.org/W2902420940","https://openalex.org/W2913086198","https://openalex.org/W2945077829","https://openalex.org/W2985153281","https://openalex.org/W3008665348"],"related_works":[],"abstract_inverted_index":{"We":[0,55],"present":[1,67],"a":[2,23,27,47,88],"quantum":[3,9,61,72,77],"eigenstate":[4,25,44],"filtering":[5],"algorithm":[6,17,58,124],"based":[7,70],"on":[8,71],"signal":[10],"processing":[11],"(QSP)":[12],"and":[13,45,66,76,91],"minimax":[14],"polynomials.":[15],"The":[16],"allows":[18],"us":[19],"to":[20,34,59],"efficiently":[21],"prepare":[22,83],"target":[24,43],"of":[26],"given":[28],"Hamiltonian,":[29],"if":[30],"we":[31],"have":[32,46],"access":[33],"an":[35],"initial":[36],"state":[37],"with":[38,41],"non-trivial":[39],"overlap":[40],"the":[42,52,60,84,93,115,120],"reasonable":[48],"lower":[49],"bound":[50],"for":[51,109],"spectral":[53],"gap.":[54],"apply":[56],"this":[57],"linear":[62],"system":[63],"problem":[64],"(QLSP),":[65],"two":[68],"algorithms":[69,82],"adiabatic":[73],"computing":[74],"(AQC)":[75],"Zeno":[78],"effect":[79],"respectively.":[80],"Both":[81],"final":[85],"solution":[86],"as":[87],"pure":[89],"state,":[90],"achieves":[92],"near":[94],"optimal<mml:math":[95],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[96],"class=\"MJX-TeXAtom-ORD\"><mml:mrow":[97],"class=\"MJX-TeXAtom-ORD\"><mml:mover><mml:mi":[98],"class=\"MJX-tex-caligraphic\"":[99,101],"mathvariant=\"script\">O</mml:mi><mml:mo":[100],"mathvariant=\"script\">~</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mo":[102],"stretchy=\"false\">(</mml:mo><mml:mi>d</mml:mi><mml:mi>\u03ba</mml:mi><mml:mi>log</mml:mi><mml:mo>\u2061</mml:mo><mml:mo":[103],"stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mrow":[104],"class=\"MJX-TeXAtom-ORD\"><mml:mo>/</mml:mo></mml:mrow><mml:mi>\u03f5</mml:mi><mml:mo":[105],"stretchy=\"false\">)</mml:mo><mml:mo":[106],"stretchy=\"false\">)</mml:mo></mml:math>query":[107],"complexity":[108],"a<mml:math":[110],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>d</mml:mi></mml:math>-sparse":[111],"matrix,":[112],"where<mml:math":[113],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03ba</mml:mi></mml:math>is":[114],"condition":[116],"number,":[117],"and<mml:math":[118],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03f5</mml:mi></mml:math>is":[119],"desired":[121],"precision.":[122],"Neither":[123],"uses":[125],"phase":[126],"estimation":[127],"or":[128],"amplitude":[129],"amplification.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":31},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2020-11-23T00:00:00"}
