{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T09:11:15Z","timestamp":1765357875573,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T00:00:00Z","timestamp":1756252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62302289","62172268","23YF1416200"],"award-info":[{"award-number":["62302289","62172268","23YF1416200"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Science and Technology Project","award":["62302289","62172268","23YF1416200"],"award-info":[{"award-number":["62302289","62172268","23YF1416200"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Detecting financial fraud is a critical aspect of modern intelligent financial systems. Despite the advances brought by deep learning in predictive accuracy, challenges persist\u2014particularly in capturing complex, high-dimensional nonlinear features. This study introduces a novel hybrid quantum recurrent neural network for fraud detection (HQRNN-FD). The model utilizes variational quantum circuits (VQCs) incorporating angle encoding, data reuploading, and hierarchical entanglement to project transaction features into quantum state spaces, thereby facilitating quantum-enhanced feature extraction. For sequential analysis, the model integrates a recurrent neural network (RNN) with a self-attention mechanism to effectively capture temporal dependencies and uncover latent fraudulent patterns. To mitigate class imbalance, the synthetic minority over-sampling technique (SMOTE) is employed during preprocessing, enhancing both class representation and model generalizability. Experimental evaluations reveal that HQRNN-FD attains an accuracy of 0.972 on publicly available fraud detection datasets, outperforming conventional models by 2.4%. In addition, the framework exhibits robustness against quantum noise and improved predictive performance with increasing qubit numbers, validating its efficacy and scalability for imbalanced financial classification tasks.<\/jats:p>","DOI":"10.3390\/e27090906","type":"journal-article","created":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T10:29:18Z","timestamp":1756376958000},"page":"906","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["HQRNN-FD: A Hybrid Quantum Recurrent Neural Network for Fraud Detection"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1474-9800","authenticated-orcid":false,"given":"Yao-Chong","family":"Li","sequence":"first","affiliation":[{"name":"College of Information Engineering, Shanghai Maritime University, 1550 Haigang Avenue, Pudong New Area, Shanghai 201306, China"},{"name":"Research Center of Intelligent Information Processing and Quantum Intelligent Computing, Shanghai Maritime University, 1550 Haigang Avenue, Pudong New Area, Shanghai 201306, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-1250-843X","authenticated-orcid":false,"given":"Yi-Fan","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Shanghai Maritime University, 1550 Haigang Avenue, Pudong New Area, Shanghai 201306, China"},{"name":"Research Center of Intelligent Information Processing and Quantum Intelligent Computing, Shanghai Maritime University, 1550 Haigang Avenue, Pudong New Area, Shanghai 201306, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9064-6304","authenticated-orcid":false,"given":"Rui-Qing","family":"Xu","sequence":"additional","affiliation":[{"name":"Faculty of Intelligence Technology, Shanghai Institute of Technology, 100 Haiquan Road, Fengxian District, Shanghai 201418, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8894-8108","authenticated-orcid":false,"given":"Ri-Gui","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Shanghai Maritime University, 1550 Haigang Avenue, Pudong New Area, Shanghai 201306, China"},{"name":"Research Center of Intelligent Information Processing and Quantum Intelligent Computing, Shanghai Maritime University, 1550 Haigang Avenue, Pudong New Area, Shanghai 201306, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4441-3355","authenticated-orcid":false,"given":"Yi-Lin","family":"Dong","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Shanghai Maritime University, 1550 Haigang Avenue, Pudong New Area, Shanghai 201306, China"},{"name":"Research Center of Intelligent Information Processing and Quantum Intelligent Computing, Shanghai Maritime University, 1550 Haigang Avenue, Pudong New Area, Shanghai 201306, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101744","DOI":"10.1016\/j.ribaf.2022.101744","article-title":"Insurance fraud detection: Evidence from artificial intelligence and machine learning","volume":"62","author":"Aslam","year":"2022","journal-title":"Res. 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