{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T19:54:47Z","timestamp":1776887687518,"version":"3.51.2"},"reference-count":53,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,6]],"date-time":"2022-12-06T00:00:00Z","timestamp":1670284800000},"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":["11975132"],"award-info":[{"award-number":["11975132"]}],"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":["61772295"],"award-info":[{"award-number":["61772295"]}],"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":["ZR2021MF049"],"award-info":[{"award-number":["ZR2021MF049"]}],"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":["ZR2019YQ01"],"award-info":[{"award-number":["ZR2019YQ01"]}],"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":["ZR202108020011"],"award-info":[{"award-number":["ZR202108020011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province, China","doi-asserted-by":"publisher","award":["11975132"],"award-info":[{"award-number":["11975132"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province, China","doi-asserted-by":"publisher","award":["61772295"],"award-info":[{"award-number":["61772295"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province, China","doi-asserted-by":"publisher","award":["ZR2021MF049"],"award-info":[{"award-number":["ZR2021MF049"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province, China","doi-asserted-by":"publisher","award":["ZR2019YQ01"],"award-info":[{"award-number":["ZR2019YQ01"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province, China","doi-asserted-by":"publisher","award":["ZR202108020011"],"award-info":[{"award-number":["ZR202108020011"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Project of Shandong Provincial Natural Science Foundation Joint Fund Application","award":["11975132"],"award-info":[{"award-number":["11975132"]}]},{"name":"Project of Shandong Provincial Natural Science Foundation Joint Fund Application","award":["61772295"],"award-info":[{"award-number":["61772295"]}]},{"name":"Project of Shandong Provincial Natural Science Foundation Joint Fund Application","award":["ZR2021MF049"],"award-info":[{"award-number":["ZR2021MF049"]}]},{"name":"Project of Shandong Provincial Natural Science Foundation Joint Fund Application","award":["ZR2019YQ01"],"award-info":[{"award-number":["ZR2019YQ01"]}]},{"name":"Project of Shandong Provincial Natural Science Foundation Joint Fund Application","award":["ZR202108020011"],"award-info":[{"award-number":["ZR202108020011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We focus on the problem that the Grover algorithm is not suitable for the completely unknown proportion of target solutions. Considering whether the existing quantum classifier used by the current quantum neural network (QNN) to complete the classification task can solve the problem of the classical classifier, this paper proposes a binary quantum neural network classifical model based on an optimized Grover algorithm based on partial diffusion. Trial and error is adopted to extend the partial diffusion quantum search algorithm with the known proportion of target solutions to the unknown state, and to apply the characteristics of the supervised learning of the quantum neural network to binary classify the classified data. Experiments show that the proposed method can effectively retrieve quantum states with similar features. The test accuracy of BQM retrieval under the depolarization noise at the 20th period can reach 97% when the depolarization rate is 0.1. It improves the retrieval accuracy by about 4% and 10% compared with MSE and BCE in the same environment.<\/jats:p>","DOI":"10.3390\/e24121783","type":"journal-article","created":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T02:18:48Z","timestamp":1670379528000},"page":"1783","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Binary Classification Quantum Neural Network Model Based on Optimized Grover Algorithm"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8204-8256","authenticated-orcid":false,"given":"Wenlin","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinuo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingjie","family":"Qu","sequence":"additional","affiliation":[{"name":"School of Science, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2680-5099","authenticated-orcid":false,"given":"Hongyang","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Science, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1899-5945","authenticated-orcid":false,"given":"Shumei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bao, Z., Zhou, J., and Tay, Y.C. (2013, January 11\u201313). sonSQL: An Extensible Relational DBMS for Social Network Start-Ups. Proceedings of the 32nd International Conference on Conceptual Modeling (ER 2013), Hong Kong, China.","DOI":"10.1007\/978-3-642-41924-9_43"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s13278-010-0011-7","article-title":"Social networks and online environments: When science and practice co-evolve","volume":"1","author":"Rosen","year":"2011","journal-title":"Soc. Netw. Anal. Min."},{"key":"ref_3","first-page":"51","article-title":"A comparative study of information diffusion in weblogs and microblogs based on social network analysis","volume":"5","author":"Zhang","year":"2012","journal-title":"Chin. J. Libr. Inf. Sci."},{"key":"ref_4","first-page":"2169","article-title":"Information Security in Big Data: Privacy and Data Mining","volume":"2","author":"Xu","year":"2014","journal-title":"Chin. J. Libr. Inf. Sci."},{"key":"ref_5","unstructured":"Witten, I., and EibeFrank (2005). Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations, China Machine Press. [1st ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1145\/1540276.1540281","article-title":"Web data mining: Exploring hyperlinks, contents, and usage data","volume":"10","author":"Nasraoui","year":"2008","journal-title":"SIGKDD Explor. Newsl."},{"key":"ref_7","first-page":"18","article-title":"Research on Decision Tree in Data Mining","volume":"8","author":"Tang","year":"2001","journal-title":"Appl. Res. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1109\/69.683753","article-title":"Efficient data mining for path traversal patterns","volume":"10","author":"Chen","year":"1998","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_9","first-page":"149","article-title":"Architecture and Technique of Multimedia Data Mining","volume":"29","author":"Juntao","year":"2003","journal-title":"Comput. Eng."},{"key":"ref_10","first-page":"38","article-title":"Data Mining Technique","volume":"6","author":"Shou","year":"2000","journal-title":"Autom.-Petro-Chem. Ind."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.drudis.2008.12.005","article-title":"Target discovery from data mining approaches","volume":"14","author":"Yang","year":"2009","journal-title":"Drug Discov. Today"},{"key":"ref_12","first-page":"873","article-title":"Mining Software Repository for Cleaning Bugs Using Data Mining Technique","volume":"69","author":"Mahmood","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1201\/9780849350351.ch7","article-title":"Machine Learning and Data Mining","volume":"42","author":"Helma","year":"2005","journal-title":"Predict. Toxicol."},{"key":"ref_14","first-page":"894205","article-title":"An Algorithm for Mining of Association Rules for the Information Communication Network Alarms Based on Swarm Intelligence","volume":"2014","author":"Wang","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"080303","DOI":"10.1088\/1674-1056\/ac05a9","article-title":"Effects of initial states on the quantum correlations in the generalized Grover search algorithm","volume":"30","author":"Chen","year":"2021","journal-title":"Chin. Phys. B"},{"key":"ref_16","unstructured":"Xu, Z., Ying, M., and Valiron, B. (2021). Reasoning about Recursive Quantum Programs. arXiv."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7643871","DOI":"10.1155\/2022\/7643871","article-title":"Quantum Information Protection Scheme Based on Reinforcement Learning for Periodic Surface Codes","volume":"2022","author":"Xue","year":"2022","journal-title":"Quantum Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"062303","DOI":"10.1103\/PhysRevA.62.062303","article-title":"Family of Grover\u2019s quantum-searching algorithms","volume":"62","author":"Galindo","year":"2000","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s11277-021-09132-5","article-title":"Development of Video Encryption Scheme Based on Quantum Controlled Dense Coding Using GHZ State for Smart Home Scenario","volume":"123","author":"Ma","year":"2022","journal-title":"Wirel. Pers. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"aaw9918","DOI":"10.1126\/sciadv.aaw9918","article-title":"Training of quantum circuits on a hybrid quantum computer","volume":"5","author":"Zhu","year":"2019","journal-title":"Sci. Adv."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"010303","DOI":"10.1088\/1674-1056\/ac11e3","article-title":"Determination of quantum toric error correction code threshold using convolutional neural network decoders","volume":"31","author":"Wang","year":"2022","journal-title":"Chin. Phys. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"e908","DOI":"10.7717\/peerj-cs.908","article-title":"Characterization inference based on joint-optimization of multi-layer semantics and deep fusion matching network","volume":"8","author":"Zheng","year":"2022","journal-title":"Peerj. Comput. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1007\/s10773-017-3601-6","article-title":"Pattern Classifications Using Grover\u2019s and Ventura\u2019s Algorithms in a Two-qubits System","volume":"57","author":"Singh","year":"2018","journal-title":"Int. J. Theor. Phys."},{"key":"ref_24","unstructured":"Huang, C.Q., Jiang, F., Huang, Q.H., Wang, X.Z., Han, Z.M., and Huang, W.Y. (2022). Dual-Graph Attention Convolution Network for 3-D Point Cloud Classification. IEEE Trans. Neural Networks Learn. Syst., 1\u201313."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ding, L., Wang, H., Wang, Y., and Wang, S. (2022). Based on Quantum Topological Stabilizer Color Code Morphism Neural Network Decoder. Quantum Eng., 2022.","DOI":"10.1155\/2022\/9638108"},{"key":"ref_26","first-page":"1","article-title":"Generalized Buffering Algorithm","volume":"99","author":"Zhou","year":"2021","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1016\/j.proeng.2011.08.244","article-title":"Quantum Neural Networks for Face Recognition Classifier","volume":"15","author":"Xu","year":"2011","journal-title":"Procedia Eng."},{"key":"ref_28","first-page":"197","article-title":"Decoherence in optimized quantum random-walk search algorithm","volume":"24","author":"Zhang","year":"2015","journal-title":"Chin. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3101","DOI":"10.1007\/s10773-012-1191-x","article-title":"Quantum Secret Sharing Based on Quantum Search Algorithm","volume":"51","author":"Tseng","year":"2012","journal-title":"Int. J. Theor. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1109\/TNNLS.2020.2980041","article-title":"A Learning Framework for n-Bit Quantized Neural Networks toward FPGAs","volume":"32","author":"Chen","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6398","DOI":"10.1007\/s10489-021-02762-z","article-title":"A polynomial kernel neural network classifier based on random sampling and information gain","volume":"52","author":"Xiao","year":"2021","journal-title":"Appl. Intell."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1002\/etep.584","article-title":"Classification of power quality disturbances using quantum neural network and DS evidence fusion","volume":"22","author":"He","year":"2012","journal-title":"Eur. Trans. Electr. Power"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1088\/1367-2630\/abdefa","article-title":"A Grover-search Based Quantum Learning Scheme for Classification","volume":"23","author":"Du","year":"2021","journal-title":"New J. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1016\/j.physd.2007.12.005","article-title":"Enhanced quantum searching via entanglement and partial diffusion","volume":"237","author":"Younes","year":"2008","journal-title":"Phys. Nonlinear Phenom."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"108982","DOI":"10.1016\/j.knosys.2022.108982","article-title":"Mapping the knowledge frontiers and evolution of decision making based on agent-based modeling","volume":"250","author":"Liang","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2120","DOI":"10.1007\/s10773-020-04485-2","article-title":"Analyzing and Improving the Secure Quantum Dialogue Protocol Based on Four-Qubit Cluster State","volume":"59","author":"Liu","year":"2020","journal-title":"Int. J. Theor. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s11128-017-1600-4","article-title":"Dynamic Grover search: Applications in recommendation systems and optimization problems","volume":"16","author":"Chakrabarty","year":"2017","journal-title":"Quantum Inf. Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1007\/s10773-022-05032-x","article-title":"Quantum Confidentiality Query Protocol Based on Bell State Identity","volume":"61","author":"Song","year":"2022","journal-title":"Int. J. Theor. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1002\/cta.619","article-title":"Neural networks with quantum architecture and quantum learning","volume":"39","author":"Panella","year":"2011","journal-title":"Int. J. Circuit Theory Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1016\/j.physa.2011.09.018","article-title":"On Grover\u2019s search algorithm from a quantum information geometry viewpoint","volume":"391","author":"Carlo","year":"2012","journal-title":"Phys. Stat. Mech. Its Appl."},{"key":"ref_41","first-page":"20","article-title":"A Modification of Grover\u2019s Quantum Search Algorithm","volume":"1","author":"Ashraf","year":"2012","journal-title":"Photonics Optoelectron"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s11704-007-0026-z","article-title":"Search an unsorted database with quantum mechanics","volume":"1","author":"Long","year":"2007","journal-title":"Front. Comput. Sci. China"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"100864","DOI":"10.1016\/j.swevo.2021.100864","article-title":"A Memetic Algorithm Based on Two_Arch2 for Multi-depot Heterogeneous-vehicle Capacitated Arc Routing Problem","volume":"63","author":"Bin","year":"2021","journal-title":"Swarm Evol. Comput."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"e353","DOI":"10.7717\/peerj-cs.353","article-title":"Joint embedding VQA model based on dynamic word vector","volume":"7","author":"Ma","year":"2021","journal-title":"Peerj Comput. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Grover, L.K. (1996, January 3\u20135). A fast quantum mechanical algorithm for database search. Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing; Association for Computing Machinery, New York, NY, USA.","DOI":"10.1145\/237814.237866"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1038\/s41534-019-0157-8","article-title":"A generative modeling approach for benchmarking and training shallow quantum circuits","volume":"5","author":"Benedetti","year":"2019","journal-title":"npj Quantum Inf."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2309","DOI":"10.1103\/PhysRevA.98.032309","article-title":"Quantum circuit learning","volume":"98","author":"Mitarai","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_48","first-page":"63","article-title":"Analysis and assessment of network security situation based on cloud model","volume":"36","author":"Zhang","year":"2014","journal-title":"Int. J. Theor. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2863","DOI":"10.1007\/s12524-021-01428-0","article-title":"Summer Maize Mapping by Compositing Time Series Sentinel-1A Imagery Based on Crop Growth Cycles","volume":"49","author":"Tian","year":"2021","journal-title":"J. Indian Soc. Remote. Sens."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"3822","DOI":"10.3390\/rs13193822","article-title":"Early-Season Mapping of Winter Crops Using Sentinel-2 Optical Imagery","volume":"13","author":"Qin","year":"2021","journal-title":"Remote. Sens."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/TR.2021.3118026","article-title":"A Comparative Study of Class Rebalancing Methods for Security Bug Report Classification","volume":"70","author":"Zheng","year":"2021","journal-title":"IEEE Trans. Reliab."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2541","DOI":"10.1109\/TSE.2021.3063727","article-title":"Data quality matters: A case study on data label correctness for security bug report prediction","volume":"48","author":"Wu","year":"2021","journal-title":"IEEE Trans. Softw. Eng."},{"key":"ref_53","first-page":"171","article-title":"Noisy Quantum Mixed State Pattern Classification Based on the Grover\u2019s Search Algorithm","volume":"15","author":"Aghayar","year":"2021","journal-title":"Int. J. Nanotechnol. Appl."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1783\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:35:00Z","timestamp":1760146500000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1783"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,6]]},"references-count":53,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["e24121783"],"URL":"https:\/\/doi.org\/10.3390\/e24121783","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,6]]}}}