{"id":"https://openalex.org/W4409145137","doi":"https://doi.org/10.3390/e27040382","title":"Finding Key Nodes in Complex Networks Through Quantum Deep Reinforcement Learning","display_name":"Finding Key Nodes in Complex Networks Through Quantum Deep Reinforcement Learning","publication_year":2025,"publication_date":"2025-04-03","ids":{"openalex":"https://openalex.org/W4409145137","doi":"https://doi.org/10.3390/e27040382","pmid":"https://pubmed.ncbi.nlm.nih.gov/40282617"},"language":"en","primary_location":{"id":"doi:10.3390/e27040382","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27040382","pdf_url":"https://www.mdpi.com/1099-4300/27/4/382/pdf?version=1743666750","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/4/382/pdf?version=1743666750","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Juechan Xiong","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Juechan Xiong","raw_affiliation_strings":["Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China","Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China","institution_ids":["https://openalex.org/I3018263800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077223066","display_name":"Xiao-Long Ren","orcid":"https://orcid.org/0000-0003-2323-163X"},"institutions":[{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiao-Long Ren","raw_affiliation_strings":["Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China"],"raw_orcid":"https://orcid.org/0000-0003-2323-163X","affiliations":[{"raw_affiliation_string":"Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China","institution_ids":["https://openalex.org/I3018263800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000969982","display_name":"Linyuan L\u00fc","orcid":"https://orcid.org/0000-0002-2156-0432"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Linyuan L\u00fc","raw_affiliation_strings":["School of Cyber Science and Technology, University of Science and Technology of China, Hefei 230026, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, University of Science and Technology of China, Hefei 230026, China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000969982","https://openalex.org/A5077223066"],"corresponding_institution_ids":["https://openalex.org/I126520041","https://openalex.org/I3018263800"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.5399,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.89534391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"27","issue":"4","first_page":"382","last_page":"382"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9973999857902527,"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":0.9955000281333923,"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/reinforcement-learning","display_name":"Reinforcement learning","score":0.7603549957275391},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7540850639343262},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.559240460395813},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5172532200813293},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.5017390251159668},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4919717013835907},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.490130752325058},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4642987847328186},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4451524019241333},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.44252899289131165},{"id":"https://openalex.org/keywords/interdependent-networks","display_name":"Interdependent networks","score":0.433931827545166},{"id":"https://openalex.org/keywords/network-science","display_name":"Network science","score":0.4331762492656708},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.4217029809951782},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.42116469144821167},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4183884859085083},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.4134988784790039},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.4085882902145386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.15147244930267334},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.08351007103919983}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.7603549957275391},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7540850639343262},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.559240460395813},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5172532200813293},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.5017390251159668},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4919717013835907},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.490130752325058},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4642987847328186},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4451524019241333},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.44252899289131165},{"id":"https://openalex.org/C101142422","wikidata":"https://www.wikidata.org/wiki/Q17101727","display_name":"Interdependent networks","level":3,"score":0.433931827545166},{"id":"https://openalex.org/C137753397","wikidata":"https://www.wikidata.org/wiki/Q2434424","display_name":"Network science","level":3,"score":0.4331762492656708},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4217029809951782},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.42116469144821167},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4183884859085083},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.4134988784790039},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4085882902145386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.15147244930267334},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.08351007103919983},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e27040382","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27040382","pdf_url":"https://www.mdpi.com/1099-4300/27/4/382/pdf?version=1743666750","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:40282617","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40282617","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:13baf87839f04c8fb4ccc3e9cf5ef687","is_oa":true,"landing_page_url":"https://doaj.org/article/13baf87839f04c8fb4ccc3e9cf5ef687","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":"Entropy, Vol 27, Iss 4, p 382 (2025)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:12025536","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12025536","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e27040382","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27040382","pdf_url":"https://www.mdpi.com/1099-4300/27/4/382/pdf?version=1743666750","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2623300173","display_name":null,"funder_award_id":"2022ZD0211400","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2659616207","display_name":null,"funder_award_id":"T2293771","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3470084698","display_name":null,"funder_award_id":"2022M710620","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6059964893","display_name":null,"funder_award_id":"STI 2030","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409145137.pdf","grobid_xml":"https://content.openalex.org/works/W4409145137.grobid-xml"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W32403112","https://openalex.org/W950821216","https://openalex.org/W1970913835","https://openalex.org/W1971421925","https://openalex.org/W1975998971","https://openalex.org/W1989400610","https://openalex.org/W1994803330","https://openalex.org/W1999634786","https://openalex.org/W2001141328","https://openalex.org/W2017990598","https://openalex.org/W2045313237","https://openalex.org/W2050401089","https://openalex.org/W2061145375","https://openalex.org/W2062021443","https://openalex.org/W2065769502","https://openalex.org/W2066636486","https://openalex.org/W2112090702","https://openalex.org/W2117941808","https://openalex.org/W2124637492","https://openalex.org/W2125315567","https://openalex.org/W2130466555","https://openalex.org/W2130476447","https://openalex.org/W2131600418","https://openalex.org/W2145339207","https://openalex.org/W2148606255","https://openalex.org/W2154851992","https://openalex.org/W2156718197","https://openalex.org/W2161685427","https://openalex.org/W2163913714","https://openalex.org/W2233066727","https://openalex.org/W2257937122","https://openalex.org/W2558748708","https://openalex.org/W2572289316","https://openalex.org/W2607264901","https://openalex.org/W2769133055","https://openalex.org/W2781738013","https://openalex.org/W2782195772","https://openalex.org/W2790388700","https://openalex.org/W2792824988","https://openalex.org/W2792946961","https://openalex.org/W2798434869","https://openalex.org/W2806889249","https://openalex.org/W2891230096","https://openalex.org/W2903221501","https://openalex.org/W2954939433","https://openalex.org/W2962756421","https://openalex.org/W2980446414","https://openalex.org/W2995067406","https://openalex.org/W3005817846","https://openalex.org/W3075559820","https://openalex.org/W3098599423","https://openalex.org/W3100408144","https://openalex.org/W3100931082","https://openalex.org/W3101122608","https://openalex.org/W3101413764","https://openalex.org/W3103589963","https://openalex.org/W3104097132","https://openalex.org/W3111162498","https://openalex.org/W3122910277","https://openalex.org/W3136233239","https://openalex.org/W3152893301","https://openalex.org/W4213009331","https://openalex.org/W4214717370","https://openalex.org/W4235019172","https://openalex.org/W4294558607","https://openalex.org/W4295138992","https://openalex.org/W4382239181","https://openalex.org/W4406261215","https://openalex.org/W6682755970","https://openalex.org/W6738964360","https://openalex.org/W6748487558","https://openalex.org/W6754582438","https://openalex.org/W6775686901"],"related_works":["https://openalex.org/W1835568051","https://openalex.org/W3194863767","https://openalex.org/W2158680676","https://openalex.org/W2190793089","https://openalex.org/W3098217834","https://openalex.org/W2187556559","https://openalex.org/W2069442775","https://openalex.org/W2963858135","https://openalex.org/W2111786937","https://openalex.org/W2545891183"],"abstract_inverted_index":{"Identifying":[0],"key":[1],"nodes":[2,37],"in":[3,9,110,129,145],"networks":[4,112,147],"is":[5,53],"a":[6,15,27],"fundamental":[7,42,143],"problem":[8],"network":[10,89,130,159],"science.":[11],"This":[12],"study":[13],"proposes":[14],"quantum":[16,29,49,149,156],"deep":[17],"reinforcement":[18,24],"learning":[19,25],"(QDRL)":[20],"framework":[21],"that":[22,101],"integrates":[23],"with":[26,83],"variational":[28],"graph":[30],"neural":[31,65],"network,":[32],"effectively":[33],"identifying":[34],"distributed":[35],"influential":[36],"while":[38],"preserving":[39],"the":[40,80,102,125,153],"network's":[41],"topological":[43],"properties.":[44],"By":[45],"leveraging":[46],"principles":[47],"of":[48,127,155],"computing,":[50],"our":[51],"method":[52],"designed":[54],"to":[55,63,123],"reduce":[56],"model":[57],"parameters":[58],"and":[59,88,95,116,133],"computational":[60],"complexity":[61],"compared":[62,79],"traditional":[64],"networks.":[66,97],"Trained":[67],"on":[68,92,114],"small":[69],"networks,":[70],"it":[71],"demonstrated":[72,120],"strong":[73],"generalization":[74],"across":[75],"diverse":[76],"scenarios.":[77],"We":[78],"proposed":[81,103],"algorithm":[82,104],"some":[84],"classical":[85],"node":[86,134],"ranking":[87],"dismantling":[90],"algorithms":[91],"various":[93],"synthetical":[94],"empirical":[96],"The":[98],"results":[99],"suggest":[100],"outperforms":[105],"existing":[106],"baseline":[107],"methods.":[108],"Moreover,":[109],"synthetic":[111],"based":[113],"Erd\u0151s-R\u00e9nyi":[115],"Watts-Strogatz":[117],"models,":[118],"QDRL":[119],"its":[121],"capability":[122],"alleviate":[124],"issue":[126],"localization":[128],"information":[131],"propagation":[132],"influence":[135],"ranking.":[136],"Our":[137],"research":[138],"provides":[139],"insights":[140],"into":[141],"addressing":[142],"problems":[144],"complex":[146],"using":[148],"machine":[150],"learning,":[151],"demonstrating":[152],"potential":[154],"approaches":[157],"for":[158],"analysis":[160],"tasks.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
