{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T16:07:21Z","timestamp":1779379641717,"version":"3.53.1"},"reference-count":50,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T00:00:00Z","timestamp":1677456000000},"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":["61901483"],"award-info":[{"award-number":["61901483"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62061136011"],"award-info":[{"award-number":["62061136011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["202001-02"],"award-info":[{"award-number":["202001-02"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["202101-15"],"award-info":[{"award-number":["202101-15"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Research Fund Program of the State Key Laboratory of High-Performance Computing","award":["61901483"],"award-info":[{"award-number":["61901483"]}]},{"name":"Research Fund Program of the State Key Laboratory of High-Performance Computing","award":["62061136011"],"award-info":[{"award-number":["62061136011"]}]},{"name":"Research Fund Program of the State Key Laboratory of High-Performance Computing","award":["202001-02"],"award-info":[{"award-number":["202001-02"]}]},{"name":"Research Fund Program of the State Key Laboratory of High-Performance Computing","award":["202101-15"],"award-info":[{"award-number":["202101-15"]}]},{"name":"Autonomous Project of the State Key Laboratory of High-Performance Computing","award":["61901483"],"award-info":[{"award-number":["61901483"]}]},{"name":"Autonomous Project of the State Key Laboratory of High-Performance Computing","award":["62061136011"],"award-info":[{"award-number":["62061136011"]}]},{"name":"Autonomous Project of the State Key Laboratory of High-Performance Computing","award":["202001-02"],"award-info":[{"award-number":["202001-02"]}]},{"name":"Autonomous Project of the State Key Laboratory of High-Performance Computing","award":["202101-15"],"award-info":[{"award-number":["202101-15"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Machine learning (ML) has achieved remarkable success in a wide range of applications. In recent ML research, deep anomaly detection (AD) has been a hot topic with the aim of discriminating among anomalous data with deep neural networks (DNNs). Notably, image AD is one of the most representative tasks in current deep AD research. ML\u2019s interaction with quantum computing is giving rise to a heated topic named quantum machine learning (QML), which enjoys great prospects according to recent academic research. This paper attempts to address the image AD problem in a deep manner with a novel QML solution. Specifically, we design a quantum-classical hybrid DNN (QHDNN) that aims to learn directly from normal raw images to train a normality model and then exclude images that do not conform to this model as anomalies during its inference. To enable the QHDNN to perform satisfactorily in deep image AD, we explore multiple quantum layer architectures and design a VQC-based QHDNN solution. Extensive experiments were conducted on commonly used benchmarks to test the proposed QML solution, whose results demonstrate the feasibility of addressing deep image AD with QML. Importantly, the experimental results show that our quantum-classical hybrid solution can even yield superior performance to that of its classical counterpart when they share the same number of learnable parameters.<\/jats:p>","DOI":"10.3390\/e25030427","type":"journal-article","created":{"date-parts":[[2023,2,28]],"date-time":"2023-02-28T02:28:09Z","timestamp":1677551289000},"page":"427","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["A Quantum-Classical Hybrid Solution for Deep Anomaly Detection"],"prefix":"10.3390","volume":"25","author":[{"given":"Maida","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anqi","family":"Huang","sequence":"additional","affiliation":[{"name":"Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0523-6816","authenticated-orcid":false,"given":"Yong","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuming","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junjie","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Siqi","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1541880.1541882","article-title":"Anomaly detection: A survey","volume":"41","author":"Chandola","year":"2009","journal-title":"Acm Comput. Surv. (Csur)"},{"key":"ref_2","unstructured":"Mirowski, P., Grimes, M.K., Malinowski, M., Hermann, K.M., Anderson, K., Teplyashin, D., Simonyan, K., Kavukcuoglu, K., Zisserman, A., and Hadsell, R. (2018). Learning to Navigate in Cities Without a Map. arXiv."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Lavin, A., and Ahmad, S. (2015, January 9\u201311). Evaluating real-time anomaly detection algorithms\u2013the Numenta anomaly benchmark. Proceedings of the 2015 IEEE 14th International Conference On Machine Learning and Applications (ICMLA), Miami, FL, USA.","DOI":"10.1109\/ICMLA.2015.141"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.cose.2008.08.003","article-title":"Anomaly-based network intrusion detection: Techniques, systems and challenges","volume":"28","year":"2009","journal-title":"Comput. Secur."},{"key":"ref_5","unstructured":"Phua, C., Lee, V., Smith, K., and Gayler, R. (2010). A comprehensive survey of data mining-based fraud detection research. arXiv."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chen, J., Qian, L., Urakov, T., Gu, W., and Liang, L. (2021, January 14\u201318). Adversarial robustness study of convolutional neural network for lumbar disk shape reconstruction from MR images. Proceedings of the SPIE Image Processing 2021: Medical Imaging: Image Processing, San Diego, CA, USA.","DOI":"10.1117\/12.2580852"},{"key":"ref_7","unstructured":"Liang, L., Ma, L., Qian, L., and Chen, J. (2020). An algorithm for out-of-distribution attack to neural network encoder. arXiv."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Schlegl, T., Seeb\u00f6ck, P., Waldstein, S.M., Schmidt-Erfurth, U., and Langs, G. (2017, January 25\u201330). Unsupervised anomaly detection with generative adversarial networks to guide marker discovery. Proceedings of the International Conference on Information Processing in Medical Imaging, Boone, NC, USA.","DOI":"10.1007\/978-3-319-59050-9_12"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"045001","DOI":"10.1088\/2058-9565\/aa8072","article-title":"Quantum autoencoders for efficient compression of quantum data","volume":"2","author":"Romero","year":"2017","journal-title":"Quantum Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"014007","DOI":"10.1088\/2058-9565\/aae22b","article-title":"Quantum autoencoders via quantum adders with genetic algorithms","volume":"4","author":"Lamata","year":"2018","journal-title":"Quantum Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1800065","DOI":"10.1002\/qute.201800065","article-title":"Experimental implementation of a quantum autoencoder via quantum adders","volume":"2","author":"Ding","year":"2019","journal-title":"Adv. Quantum Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"062327","DOI":"10.1103\/PhysRevA.96.062327","article-title":"Tomography and generative training with quantum Boltzmann machines","volume":"96","author":"Wiebe","year":"2017","journal-title":"Phys. Rev."},{"key":"ref_13","first-page":"1088","article-title":"Quantum and classical machine learning for the classification of non-small-cell lung cancer patients","volume":"2","author":"Jain","year":"2020","journal-title":"Appl. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"012324","DOI":"10.1103\/PhysRevA.98.012324","article-title":"Quantum generative adversarial networks","volume":"98","author":"Killoran","year":"2018","journal-title":"Phys. Rev."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"040502.1","DOI":"10.1103\/PhysRevLett.121.040502","article-title":"Quantum Generative Adversarial Learning","volume":"121","author":"Lloyd","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2000003","DOI":"10.1002\/qute.202000003","article-title":"Variational quantum generators: Generative adversarial quantum machine learning for continuous distributions","volume":"4","author":"Romero","year":"2021","journal-title":"Adv. Quantum Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"052306","DOI":"10.1103\/PhysRevA.99.052306","article-title":"Learning and inference on generative adversarial quantum circuits","volume":"99","author":"Zeng","year":"2019","journal-title":"Phys. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"130503","DOI":"10.1103\/PhysRevLett.113.130503","article-title":"Quantum support vector machine for big data classification","volume":"113","author":"Rebentrost","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s42484-019-00007-4","article-title":"Kernel methods in quantum machine learning","volume":"1","author":"Mengoni","year":"2019","journal-title":"Quantum Mach. Intell."},{"key":"ref_20","first-page":"1","article-title":"Power of data in quantum machine learning","volume":"12","author":"Huang","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_21","unstructured":"Ruff, L., Vandermeulen, R.A., G\u00f6rnitz, N., Deecke, L., and Kloft, M. (2018, January 10\u201315). Deep One-Class Classification. Proceedings of the International Conference on Machine Learning, Stockholm, Sweden."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1017\/S026988891300043X","article-title":"One-class classification: Taxonomy of study and review of techniques","volume":"29","author":"Khan","year":"2014","journal-title":"Knowl. Eng. Rev."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1214\/aoms\/1177704472","article-title":"On estimation of a probability density function and mode","volume":"33","author":"Parzen","year":"1962","journal-title":"Ann. Math. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1162\/089976601750264965","article-title":"Estimating the support of a high-dimensional distribution","volume":"13","author":"Platt","year":"2001","journal-title":"Neural Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1023\/B:MACH.0000008084.60811.49","article-title":"Support vector data description","volume":"54","author":"Tax","year":"2004","journal-title":"Mach. Learn."},{"key":"ref_26","first-page":"777","article-title":"One-class LP classifiers for dissimilarity representations","volume":"15","author":"Pekalska","year":"2003","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.neunet.2014.09.003","article-title":"Deep learning in neural networks: An overview","volume":"61","author":"Schmidhuber","year":"2015","journal-title":"Neural Netw."},{"key":"ref_29","first-page":"1","article-title":"Variational autoencoder based anomaly detection using reconstruction probability","volume":"2","author":"Jinwon","year":"2015","journal-title":"Spec. Lect."},{"key":"ref_30","first-page":"9758","article-title":"Deep anomaly detection using geometric transformations","volume":"31","author":"Golan","year":"2018","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_31","first-page":"11839","article-title":"Csi: Novelty detection via contrastive learning on distributionally shifted instances","volume":"33","author":"Tack","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42484-020-00025-7","article-title":"Universal discriminative quantum neural networks","volume":"3","author":"Chen","year":"2021","journal-title":"Quantum Mach. Intell."},{"key":"ref_33","unstructured":"Wilson, C., Otterbach, J., Tezak, N., Smith, R., Polloreno, A., Karalekas, P.J., Heidel, S., Alam, M.S., Crooks, G., and da Silva, M. (2018). Quantum kitchen sinks: An algorithm for machine learning on near-term quantum computers. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42484-020-00036-4","article-title":"Layerwise learning for quantum neural networks","volume":"3","author":"Skolik","year":"2021","journal-title":"Quantum Mach. Intell."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"340","DOI":"10.22331\/q-2020-10-09-340","article-title":"Transfer learning in hybrid classical-quantum neural networks","volume":"4","author":"Mari","year":"2020","journal-title":"Quantum"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Park, G., Huh, J., and Park, D.K. (2022). Variational quantum one-class classifier. arXiv.","DOI":"10.1088\/2632-2153\/acafd5"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s42484-022-00075-z","article-title":"Hybrid classical-quantum autoencoder for anomaly detection","volume":"4","author":"Sakhnenko","year":"2022","journal-title":"Quantum Mach. Intell."},{"key":"ref_38","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1038\/s41567-019-0648-8","article-title":"Quantum convolutional neural networks","volume":"15","author":"Cong","year":"2019","journal-title":"Nat. Phys."},{"key":"ref_40","unstructured":"Farhi, E., and Neven, H. (2018). Classification with quantum neural networks on near term processors. arXiv."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"033063","DOI":"10.1103\/PhysRevResearch.1.033063","article-title":"Continuous-variable quantum neural networks","volume":"1","author":"Killoran","year":"2019","journal-title":"Phys. Rev. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"023023","DOI":"10.1088\/1367-2630\/18\/2\/023023","article-title":"The theory of variational hybrid quantum-classical algorithms","volume":"18","author":"McClean","year":"2016","journal-title":"New J. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"220301","DOI":"10.1007\/s11433-021-1793-6","article-title":"Recent advances for quantum classifiers","volume":"65","author":"Li","year":"2022","journal-title":"Sci. China Physics, Mech. Astron."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"677","DOI":"10.22331\/q-2022-03-30-677","article-title":"General parameter-shift rules for quantum gradients","volume":"6","author":"Wierichs","year":"2022","journal-title":"Quantum"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","article-title":"Quantum Computing in the NISQ era and beyond","volume":"2","author":"Preskill","year":"2018","journal-title":"Quantum"},{"key":"ref_46","unstructured":"Shalev-Shwartz, S., Shamir, O., and Shammah, S. (2017, January 6\u201311). Failures of gradient-based deep learning. Proceedings of the International Conference on Machine Learning, PMLR, Sydney, Australia."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.patcog.2016.03.028","article-title":"High-dimensional and large-scale anomaly detection using a linear one-class SVM with deep learning","volume":"58","author":"Erfani","year":"2016","journal-title":"Pattern Recognit."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1109\/JSTARS.2021.3134785","article-title":"On circuit-based hybrid quantum neural networks for remote sensing imagery classification","volume":"15","author":"Sebastianelli","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Zeng, Y., Wang, H., He, J., Huang, Q., and Chang, S. (2022). A Multi-Classification Hybrid Quantum Neural Network Using an All-Qubit Multi-Observable Measurement Strategy. Entropy, 24.","DOI":"10.3390\/e24030394"},{"key":"ref_50","unstructured":"Smith, R.S., Curtis, M.J., and Zeng, W.J. (2016). A practical quantum instruction set architecture. arXiv."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/3\/427\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:43:44Z","timestamp":1760121824000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/3\/427"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,27]]},"references-count":50,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["e25030427"],"URL":"https:\/\/doi.org\/10.3390\/e25030427","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,27]]}}}