{"id":"https://openalex.org/W4406549332","doi":"https://doi.org/10.22331/q-2026-03-16-2031","title":"A posteriori error estimates for the Lindblad master equation","display_name":"A posteriori error estimates for the Lindblad master equation","publication_year":2026,"publication_date":"2026-03-16","ids":{"openalex":"https://openalex.org/W4406549332","doi":"https://doi.org/10.22331/q-2026-03-16-2031"},"language":"en","primary_location":{"id":"doi:10.22331/q-2026-03-16-2031","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-03-16-2031","pdf_url":"https://quantum-journal.org/papers/q-2026-03-16-2031/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","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2026-03-16-2031/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115926677","display_name":"Paul-Louis Etienney","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210103330","display_name":"\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/01dp7jr64","country_code":"BI","type":"education","lineage":["https://openalex.org/I4210103330"]},{"id":"https://openalex.org/I4210129651","display_name":"Laboratoire de Physique de l'Ecole Normale Sup\u00e9rieure","ror":"https://ror.org/03a26mh11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I2746051580","https://openalex.org/I2746051580","https://openalex.org/I2800004676","https://openalex.org/I29607241","https://openalex.org/I39804081","https://openalex.org/I4210129651"]}],"countries":["BI","FR"],"is_corresponding":false,"raw_author_name":"Paul-Louis Etienney","raw_affiliation_strings":["Laboratoire de Physique de l&apos;\u00c9cole Normale Sup\u00e9rieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Universit\u00e9, PSL Research University, Paris, France","LPENS - Laboratoire de physique de l'ENS - ENS Paris (24, rue Lhomond\r\n75005 Paris - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique de l&apos;\u00c9cole Normale Sup\u00e9rieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Universit\u00e9, PSL Research University, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I29607241","https://openalex.org/I39804081","https://openalex.org/I4210103330"]},{"raw_affiliation_string":"LPENS - Laboratoire de physique de l'ENS - ENS Paris (24, rue Lhomond\r\n75005 Paris - France)","institution_ids":["https://openalex.org/I29607241","https://openalex.org/I4210129651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091002355","display_name":"R\u00e9mi Robin","orcid":"https://orcid.org/0000-0001-5609-1659"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210103330","display_name":"\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/01dp7jr64","country_code":"BI","type":"education","lineage":["https://openalex.org/I4210103330"]}],"countries":["BI","FR"],"is_corresponding":false,"raw_author_name":"R\u00e9mi Robin","raw_affiliation_strings":["Laboratoire de Physique de l&apos;\u00c9cole Normale Sup\u00e9rieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Universit\u00e9, PSL Research University, Paris, France","QUANTIC - QUANTum Information Circuits (45, rue d'Ulm 75230 Paris Cedex 05 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique de l&apos;\u00c9cole Normale Sup\u00e9rieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Universit\u00e9, PSL Research University, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I29607241","https://openalex.org/I39804081","https://openalex.org/I4210103330"]},{"raw_affiliation_string":"QUANTIC - QUANTum Information Circuits (45, rue d'Ulm 75230 Paris Cedex 05 - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065752316","display_name":"Pierre Rouchon","orcid":"https://orcid.org/0000-0001-6160-5634"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210103330","display_name":"\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/01dp7jr64","country_code":"BI","type":"education","lineage":["https://openalex.org/I4210103330"]}],"countries":["BI","FR"],"is_corresponding":false,"raw_author_name":"Pierre Rouchon","raw_affiliation_strings":["Laboratoire de Physique de l&apos;\u00c9cole Normale Sup\u00e9rieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Universit\u00e9, PSL Research University, Paris, France","QUANTIC - QUANTum Information Circuits (45, rue d'Ulm 75230 Paris Cedex 05 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique de l&apos;\u00c9cole Normale Sup\u00e9rieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Universit\u00e9, PSL Research University, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I29607241","https://openalex.org/I39804081","https://openalex.org/I4210103330"]},{"raw_affiliation_string":"QUANTIC - QUANTum Information Circuits (45, rue d'Ulm 75230 Paris Cedex 05 - France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00749897,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":null,"first_page":"2031","last_page":"2031"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11177","display_name":"Spectroscopy and Quantum Chemical Studies","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T11177","display_name":"Spectroscopy and Quantum Chemical Studies","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/master-equation","display_name":"Master equation","score":0.7350984215736389},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6726234555244446},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5169048309326172},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48895204067230225},{"id":"https://openalex.org/keywords/maximum-a-posteriori-estimation","display_name":"Maximum a posteriori estimation","score":0.44842272996902466},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.37227320671081543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34221380949020386},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3313238322734833},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.22256317734718323},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.18198105692863464},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.1703142523765564},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.168730229139328},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.1039549708366394},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06717145442962646}],"concepts":[{"id":"https://openalex.org/C128805008","wikidata":"https://www.wikidata.org/wiki/Q722878","display_name":"Master equation","level":3,"score":0.7350984215736389},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6726234555244446},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5169048309326172},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48895204067230225},{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.44842272996902466},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.37227320671081543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34221380949020386},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3313238322734833},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.22256317734718323},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.18198105692863464},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.1703142523765564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.168730229139328},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.1039549708366394},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06717145442962646},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.22331/q-2026-03-16-2031","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-03-16-2031","pdf_url":"https://quantum-journal.org/papers/q-2026-03-16-2031/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:2501.09607","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.09607","pdf_url":"https://arxiv.org/pdf/2501.09607","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2501.09607","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:HAL:hal-04990411v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04990411","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2025","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:doaj.org/article:38893dbf70614804acff51cc7d305694","is_oa":true,"landing_page_url":"https://doaj.org/article/38893dbf70614804acff51cc7d305694","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":"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 10, p 2031 (2026)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2501.09607","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2501.09607","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.22331/q-2026-03-16-2031","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-03-16-2031","pdf_url":"https://quantum-journal.org/papers/q-2026-03-16-2031/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/G5521806082","display_name":"From NISQ to LSQ: Bosonic and LDPC codes","funder_award_id":"ANR-22-PETQ-0006","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406549332.pdf","grobid_xml":"https://content.openalex.org/works/W4406549332.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W4409880682","https://openalex.org/W4417323120","https://openalex.org/W2963113220","https://openalex.org/W1578322733","https://openalex.org/W4405126324","https://openalex.org/W2094453790","https://openalex.org/W2038944277","https://openalex.org/W2765389212","https://openalex.org/W1998916018","https://openalex.org/W4405715546","https://openalex.org/W4404992476","https://openalex.org/W2032839191","https://openalex.org/W1984125696","https://openalex.org/W4361001537","https://openalex.org/W2154196599","https://openalex.org/W2566706182","https://openalex.org/W2025744050","https://openalex.org/W2730459202","https://openalex.org/W2015683881","https://openalex.org/W2068006129","https://openalex.org/W4408319761","https://openalex.org/W4387905414","https://openalex.org/W4404536332","https://openalex.org/W4406696431","https://openalex.org/W4296680572","https://openalex.org/W2530247960","https://openalex.org/W1863385632"],"related_works":["https://openalex.org/W2073801793","https://openalex.org/W2111360083","https://openalex.org/W2084270479","https://openalex.org/W2512311442","https://openalex.org/W2088068170","https://openalex.org/W4281381736","https://openalex.org/W2150865841","https://openalex.org/W2138865713","https://openalex.org/W2169353922","https://openalex.org/W3137869026"],"abstract_inverted_index":{"We":[0],"are":[1],"interested":[2],"in":[3,16,46,113],"the":[4,12,23,28,38,61,81,84,92,99,102,114,118,131,134,143,160],"simulation":[5],"of":[6,25,83,94,101,117,133,142,159,162],"open":[7],"quantum":[8],"systems":[9],"governed":[10],"by":[11,125],"Lindblad":[13,119],"master":[14],"equation":[15,45],"an":[17,164],"infinite-dimensional":[18],"Hilbert":[19,39,135],"space.":[20,136],"To":[21],"simulate":[22],"solution":[24,59],"this":[26,65,123,149],"equation,":[27,120],"standard":[29],"approach":[30,124,150],"involves":[31],"two":[32,72],"sequential":[33],"approximations:":[34],"first,":[35],"we":[36,51,67,90,121],"truncate":[37],"space":[40],"to":[41,55,60,79,128,176],"derive":[42],"a":[43,47,57,110,169],"differential":[44],"finite-dimensional":[48,62],"subspace.":[49],"Then,":[50],"use":[52],"discrete":[53],"time-step":[54],"obtain":[56],"numerical":[58,85,88],"evolution.":[63],"In":[64],"paper,":[66],"establish":[68],"bounds":[69],"for":[70],"these":[71],"approximations":[73],"that":[74],"can":[75,151],"be":[76],"explicitly":[77],"computed":[78],"guarantee":[80],"accuracy":[82],"results.":[86],"Through":[87],"examples,":[89],"demonstrate":[91],"efficiency":[93],"our":[95,172],"method,":[96],"empirically":[97],"highlighting":[98],"tightness":[100],"upper":[103],"bound.":[104],"While":[105],"adaptive":[106,140],"time-stepping":[107],"is":[108],"already":[109],"common":[111],"practice":[112],"time":[115,155],"discretization":[116],"extend":[122],"showing":[126],"how":[127],"dynamically":[129],"adjust":[130],"truncation":[132],"This":[137],"enables":[138],"fully":[139],"simulations":[141],"density":[144],"matrix.":[145],"For":[146],"large-scale":[147],"simulations,":[148],"significantly":[152],"reduce":[153],"computational":[154],"and":[156],"relieves":[157],"users":[158],"challenge":[161],"selecting":[163],"appropriate":[165],"truncation.":[166],"Furthermore,":[167],"as":[168],"special":[170],"case,":[171],"method":[173],"naturally":[174],"applies":[175],"Hamiltonian":[177],"(unitary)":[178],"dynamics.":[179]},"counts_by_year":[],"updated_date":"2026-07-26T07:53:14.480251","created_date":"2025-01-18T00:00:00"}
