{"id":"https://openalex.org/W4224096378","doi":"https://doi.org/10.22331/q-2022-04-15-690","title":"Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr\u00f6dinger Equation","display_name":"Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr\u00f6dinger Equation","publication_year":2022,"publication_date":"2022-04-15","ids":{"openalex":"https://openalex.org/W4224096378","doi":"https://doi.org/10.22331/q-2022-04-15-690"},"language":"en","primary_location":{"id":"doi:10.22331/q-2022-04-15-690","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-15-690","pdf_url":"https://quantum-journal.org/papers/q-2022-04-15-690/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-2022-04-15-690/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025855125","display_name":"Dong An","orcid":"https://orcid.org/0000-0002-2964-3603"},"institutions":[{"id":"https://openalex.org/I4210108409","display_name":"Joint Center for Quantum Information and Computer Science","ror":"https://ror.org/02048n894","country_code":"US","type":"facility","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065","https://openalex.org/I4210108409","https://openalex.org/I66946132"]},{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dong An","raw_affiliation_strings":["Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland, College Park, MD 20742, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I4210108409","https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071221629","display_name":"Di Fang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210107338","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338"]},{"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":"Di Fang","raw_affiliation_strings":["Challenge Institute for Quantum Computation, University of California, Berkeley, CA 94720, USA","Department of Mathematics, University of California, Berkeley, CA 94720, USA","Simons Institute for the Theory of Computing, University of California, Berkeley, CA 94720, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Challenge Institute for Quantum Computation, University of California, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Simons Institute for the Theory of Computing, University of California, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I4210107338","https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107195431","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":false,"raw_author_name":"Lin Lin","raw_affiliation_strings":["Challenge Institute for Quantum Computation, University of California, Berkeley, CA 94720, USA","Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA","Department of Mathematics, University of California, Berkeley, CA 94720, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Challenge Institute for Quantum Computation, University of California, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025855125"],"corresponding_institution_ids":["https://openalex.org/I4210108409","https://openalex.org/I66946132"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":4.439,"has_fulltext":true,"cited_by_count":37,"citation_normalized_percentile":{"value":0.95010641,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"6","issue":null,"first_page":"690","last_page":"690"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9983999729156494,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9950000047683716,"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/superconvergence","display_name":"Superconvergence","score":0.8259870409965515},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.8178690075874329},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.557371973991394},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49457618594169617},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.4767378568649292},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4733923673629761},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46686577796936035},{"id":"https://openalex.org/keywords/commutator","display_name":"Commutator","score":0.4572739899158478},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.45358943939208984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2868732810020447},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26337140798568726},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25900137424468994},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.22189128398895264},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.17331305146217346},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16919460892677307},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11858603358268738},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.11371123790740967},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08021390438079834}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.8259870409965515},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.8178690075874329},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.557371973991394},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49457618594169617},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4767378568649292},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4733923673629761},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46686577796936035},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.4572739899158478},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.45358943939208984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2868732810020447},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26337140798568726},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25900137424468994},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22189128398895264},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.17331305146217346},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16919460892677307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11858603358268738},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.11371123790740967},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08021390438079834},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.22331/q-2022-04-15-690","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-15-690","pdf_url":"https://quantum-journal.org/papers/q-2022-04-15-690/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:2111.03103","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.03103","pdf_url":"https://arxiv.org/pdf/2111.03103","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:osti.gov:1881872","is_oa":true,"landing_page_url":"https://www.osti.gov/servlets/purl/1881872","pdf_url":"https://www.osti.gov/biblio/1881872","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},{"id":"pmh:ark:/13030/qt2174t1wq","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:doaj.org/article:e76daf269b5d4777bc7157a5718f8abd","is_oa":false,"landing_page_url":"https://doaj.org/article/e76daf269b5d4777bc7157a5718f8abd","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 6, p 690 (2022)","raw_type":"article"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt2174t1wq","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/2174t1wq","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":"Quantum, vol 6","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2022-04-15-690","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-15-690","pdf_url":"https://quantum-journal.org/papers/q-2022-04-15-690/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/G3077665131","display_name":null,"funder_award_id":"2016245","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G371001046","display_name":null,"funder_award_id":"DMS-1652330","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G394576491","display_name":null,"funder_award_id":"OMA-2016245","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4064939977","display_name":"CAREER: Turbo-Charging Hybrid Functional Electronic Structure Calculations via Adaptive Compression Methods","funder_award_id":"1652330","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"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"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4224096378.pdf","grobid_xml":"https://content.openalex.org/works/W4224096378.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W1595515622","https://openalex.org/W1624156688","https://openalex.org/W1871899311","https://openalex.org/W1973055673","https://openalex.org/W1973942282","https://openalex.org/W1980829476","https://openalex.org/W1985671429","https://openalex.org/W2023232348","https://openalex.org/W2030839599","https://openalex.org/W2039763880","https://openalex.org/W2053987271","https://openalex.org/W2064906820","https://openalex.org/W2067911745","https://openalex.org/W2081161648","https://openalex.org/W2097174474","https://openalex.org/W2113404591","https://openalex.org/W2114599246","https://openalex.org/W2117302943","https://openalex.org/W2167110831","https://openalex.org/W2415656260","https://openalex.org/W2514611406","https://openalex.org/W2535738892","https://openalex.org/W2551630517","https://openalex.org/W2564229214","https://openalex.org/W2737425023","https://openalex.org/W2766294686","https://openalex.org/W2769838435","https://openalex.org/W2775106578","https://openalex.org/W2795534239","https://openalex.org/W2799222224","https://openalex.org/W2803843259","https://openalex.org/W2805612073","https://openalex.org/W2851910911","https://openalex.org/W2901677314","https://openalex.org/W2908019568","https://openalex.org/W2951814536","https://openalex.org/W2953096107","https://openalex.org/W2963652075","https://openalex.org/W2964307732","https://openalex.org/W2995050112","https://openalex.org/W2998232945","https://openalex.org/W3033362905","https://openalex.org/W3046826898","https://openalex.org/W3098107311","https://openalex.org/W3098640891","https://openalex.org/W3098852652","https://openalex.org/W3098935501","https://openalex.org/W3101824094","https://openalex.org/W3104433882","https://openalex.org/W3105081351","https://openalex.org/W3116683544","https://openalex.org/W3145689608","https://openalex.org/W3164090400","https://openalex.org/W3198317698","https://openalex.org/W3202536522","https://openalex.org/W3213044520","https://openalex.org/W4231706539","https://openalex.org/W4243647189","https://openalex.org/W4244980514","https://openalex.org/W4255754126","https://openalex.org/W6630499640"],"related_works":["https://openalex.org/W2094577950","https://openalex.org/W2031157121","https://openalex.org/W1565666028","https://openalex.org/W2891538916","https://openalex.org/W4230524683","https://openalex.org/W3141012097","https://openalex.org/W4233029528","https://openalex.org/W2977168711","https://openalex.org/W2756533014","https://openalex.org/W49167663"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,80,92],"simple":[3],"quantum":[4,10,17,31],"algorithm":[5,32],"for":[6,20,54,67],"simulating":[7],"highly":[8],"oscillatory":[9],"dynamics,":[11],"which":[12,87],"does":[13],"not":[14],"require":[15],"complicated":[16],"control":[18],"logic":[19],"handling":[21],"time-ordering":[22],"operators.":[23],"To":[24],"our":[25,74,108],"knowledge,":[26],"this":[27],"is":[28,34],"the":[29,38,42,59,68,71,88,101,104],"first":[30],"that":[33,66],"both":[35],"insensitive":[36],"to":[37],"rapid":[39],"changes":[40],"of":[41,70,86,95,107],"time-dependent":[43],"Hamiltonian":[44,56],"and":[45,78,103],"exhibits":[46,76],"commutator":[47],"scaling.":[48],"Our":[49],"method":[50,75],"can":[51],"be":[52],"used":[53],"efficient":[55],"simulation":[57,69],"in":[58],"interaction":[60],"picture.":[61],"In":[62],"particular,":[63],"we":[64],"demonstrate":[65],"Schr\u00f6dinger":[72],"equation,":[73],"superconvergence":[77,105],"achieves":[79],"surprising":[81],"second":[82],"order":[83],"convergence":[84],"rate,":[85],"proof":[89],"rests":[90],"on":[91],"careful":[93],"application":[94],"pseudo-differential":[96],"calculus.":[97],"Numerical":[98],"results":[99],"verify":[100],"effectiveness":[102],"property":[106],"method.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}