{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T12:27:21Z","timestamp":1782736041911,"version":"3.54.5"},"reference-count":56,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T00:00:00Z","timestamp":1751932800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62302289"],"award-info":[{"award-number":["62302289"]}]},{"name":"National Natural Science Foundation of China","award":["62172268"],"award-info":[{"award-number":["62172268"]}]},{"name":"National Natural Science Foundation of China","award":["23YF1416200"],"award-info":[{"award-number":["23YF1416200"]}]},{"name":"Shanghai Science and Technology Project","award":["62302289"],"award-info":[{"award-number":["62302289"]}]},{"name":"Shanghai Science and Technology Project","award":["62172268"],"award-info":[{"award-number":["62172268"]}]},{"name":"Shanghai Science and Technology Project","award":["23YF1416200"],"award-info":[{"award-number":["23YF1416200"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum neural networks (QNNs) represent an emerging technology that uses a quantum computer for neural network computations. The QNNs have demonstrated potential advantages over classical neural networks in certain tasks. As a core component of a QNN, the parameterized quantum circuit (PQC) plays a crucial role in determining the QNN\u2019s overall performance. However, quantum circuit architectures designed manually based on experience or using specific hardware structures can suffer from inefficiency due to the introduction of redundant quantum gates, which amplifies the impact of noise on system performance. Recent studies have suggested that the advantages of quantum evolutionary algorithms (QEAs) in terms of precision and convergence speed can provide an effective solution to quantum circuit architecture-related problems. Currently, most QEAs adopt a fixed rotation mode in the evolution process, and a lack of an adaptive updating mode can cause the QEAs to fall into a local optimum and make it difficult for them to converge. To address these problems, this study proposes an adaptive quantum evolution algorithm (AQEA). First, an adaptive mechanism is introduced to the evolution process, and the strategy of combining two dynamic rotation angles is adopted. Second, to prevent the fluctuations of the population\u2019s offspring, the elite retention of the parents is used to ensure the inheritance of good genes. Finally, when the population falls into a local optimum, a quantum catastrophe mechanism is employed to break the current population state. The experimental results show that compared with the QNN structure based on manual design and QEA search, the proposed AQEA can reduce the number of network parameters by up to 20% and increase the accuracy by 7.21%. Moreover, in noisy environments, the AQEA-optimized circuit outperforms traditional circuits in maintaining high fidelity, and its excellent noise resistance provides strong support for the reliability of quantum computing.<\/jats:p>","DOI":"10.3390\/e27070733","type":"journal-article","created":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T07:31:57Z","timestamp":1751959917000},"page":"733","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["AQEA-QAS: An Adaptive Quantum Evolutionary Algorithm for Quantum Architecture Search"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1474-9800","authenticated-orcid":false,"given":"Yaochong","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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8894-8108","authenticated-orcid":false,"given":"Rigui","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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Qu","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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9064-6304","authenticated-orcid":false,"given":"Ruiqing","family":"Xu","sequence":"additional","affiliation":[{"name":"Faculty of Intelligence Technology, Shanghai Institute of Technology, 100 Haiquan Road, Fengxian District, Shanghai 201418, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S1076-5670(08)70147-2","article-title":"Quantum Neural Computing","volume":"94","author":"Kak","year":"1995","journal-title":"Adv. Imaging Electron Phys."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hogg, T. (1995). Quantum Computing and Phase Transitions in Combinatorial Search. arXiv.","DOI":"10.1613\/jair.204"},{"key":"ref_3","unstructured":"Shor, P. (1994, January 20\u201322). Algorithms for quantum computation: Discrete logarithms and factoring. Proceedings of the Proceedings 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, USA."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1098\/rspa.1998.0166","article-title":"Resilient quantum computation: Error models and thresholds","volume":"454","author":"Knill","year":"1998","journal-title":"Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"key":"ref_5","unstructured":"Farhi, E., Goldstone, J., and Gutmann, S. (2014). A Quantum Approximate Optimization Algorithm. arXiv."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"020319","DOI":"10.1103\/PRXQuantum.1.020319","article-title":"Exploring Entanglement and Optimization within the Hamiltonian Variational Ansatz","volume":"1","author":"Wiersema","year":"2020","journal-title":"PRX Quantum"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"010309","DOI":"10.1103\/PRXQuantum.2.010309","article-title":"Quantifying the Efficiency of State Preparation via Quantum Variational Eigensolvers","volume":"2","author":"Matos","year":"2021","journal-title":"PRX Quantum"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"013015","DOI":"10.1088\/1367-2630\/acb22c","article-title":"Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry","volume":"25","author":"Sun","year":"2023","journal-title":"New J. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1038\/s41586-019-0980-2","article-title":"Supervised learning with quantum-enhanced feature spaces","volume":"567","author":"Temme","year":"2019","journal-title":"Nature"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4213","DOI":"10.1038\/ncomms5213","article-title":"A variational eigenvalue solver on a photonic quantum processor","volume":"5","author":"Peruzzo","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"043001","DOI":"10.1088\/2058-9565\/ab4eb5","article-title":"Parameterized quantum circuits as machine learning models","volume":"4","author":"Benedetti","year":"2019","journal-title":"Quantum Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4812","DOI":"10.1038\/s41467-018-07090-4","article-title":"Barren plateaus in quantum neural network training landscapes","volume":"9","author":"McClean","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1038\/s41467-021-21728-w","article-title":"Cost function dependent barren plateaus in shallow parametrized quantum circuits","volume":"12","author":"Cerezo","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_14","first-page":"041011","article-title":"Absence of Barren Plateaus in Quantum Convolutional Neural Networks","volume":"11","author":"Pesah","year":"2021","journal-title":"Phys. Rev. X"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"180505","DOI":"10.1103\/PhysRevLett.128.180505","article-title":"Trainability of Dissipative Perceptron-Based Quantum Neural Networks","volume":"128","author":"Sharma","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Martyniuk, D., Jung, J., and Paschke, A. (2024, January 15\u201320). Quantum Architecture Search: A Survey. Proceedings of the 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), Montreal, QC, Canada.","DOI":"10.1109\/QCE60285.2024.00198"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhu, W., Pi, J., and Peng, Q. (2023, January 22\u201324). A Brief Survey of Quantum Architecture Search. Proceedings of the 6th International Conference on Algorithms, Computing and Systems, Sanya, China. ICACS \u201922.","DOI":"10.1145\/3564982.3564989"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"391","DOI":"10.22331\/q-2021-01-28-391","article-title":"Structure optimization for parameterized quantum circuits","volume":"5","author":"Ostaszewski","year":"2021","journal-title":"Quantum"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s42484-023-00132-1","article-title":"A semi-agnostic ansatz with variable structure for variational quantum algorithms","volume":"5","author":"Bilkis","year":"2023","journal-title":"Quantum Mach. Intell."},{"key":"ref_20","unstructured":"Pointing, J., Padon, O., Jia, Z., Ma, H., Hirth, A., Palsberg, J., and Aiken, A. (2021). Quanto: Optimizing Quantum Circuits with Automatic Generation of Circuit Identities. arXiv."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"010324","DOI":"10.1103\/PRXQuantum.2.010324","article-title":"Machine Learning of Noise-Resilient Quantum Circuits","volume":"2","author":"Cincio","year":"2021","journal-title":"PRX Quantum"},{"key":"ref_22","unstructured":"Zhu, P., Ding, W., Wei, L., Guan, Z., and Feng, S. (2021). A Variation-Aware Quantum Circuit Mapping Approach Based on Multi-agent Cooperation. arXiv."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"023074","DOI":"10.1103\/PhysRevResearch.2.023074","article-title":"Quantum optimization with a novel Gibbs objective function and ansatz architecture search","volume":"2","author":"Li","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"140","DOI":"10.22331\/q-2019-05-13-140","article-title":"Quantum-assisted quantum compiling","volume":"3","author":"Khatri","year":"2019","journal-title":"Quantum"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"033002","DOI":"10.1088\/1367-2630\/abe0ae","article-title":"Variational quantum compiling with double Q-learning","volume":"23","author":"He","year":"2021","journal-title":"New J. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"170501","DOI":"10.1103\/PhysRevLett.125.170501","article-title":"Topological Quantum Compiling with Reinforcement Learning","volume":"125","author":"Zhang","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","unstructured":"Ostaszewski, M., Trenkwalder, L.M., Masarczyk, W., Scerri, E., and Dunjko, V. (2021). Reinforcement learning for optimization of variational quantum circuit architectures. arXiv."},{"key":"ref_28","unstructured":"Kuo, E.J., Fang, Y.L.L., and Chen, S.Y.C. (2021). Quantum Architecture Search via Deep Reinforcement Learning. arXiv."},{"key":"ref_29","unstructured":"Chivilikhin, D., Samarin, A., Ulyantsev, V., Iorsh, I., Oganov, A.R., and Kyriienko, O. (2020). MoG-VQE: Multiobjective genetic variational quantum eigensolver. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"052414","DOI":"10.1103\/PhysRevA.105.052414","article-title":"Robust resource-efficient quantum variational ansatz through an evolutionary algorithm","volume":"105","author":"Huang","year":"2022","journal-title":"Phys. Rev. A"},{"key":"ref_31","unstructured":"Rattew, A.G., Hu, S., Pistoia, M., Chen, R., and Wood, S. (2020). A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver. arXiv."},{"key":"ref_32","unstructured":"Nielsen, M.A., and Chuang, I.L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition, Cambridge University Press."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Schuld, M., Sinayskiy, I., and Petruccione, F. (2014). Quantum computing for pattern classification. arXiv.","DOI":"10.1007\/978-3-319-13560-1_17"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Wang, H., Ding, Y., Gu, J., Lin, Y., Pan, D.Z., Chong, F.T., and Han, S. (2022, January 2\u20136). QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits. Proceedings of the 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA), Seoul, Republic of Korea.","DOI":"10.1109\/HPCA53966.2022.00057"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"045027","DOI":"10.1088\/2632-2153\/ac28dd","article-title":"Neural predictor based quantum architecture search","volume":"2","author":"Zhang","year":"2021","journal-title":"Mach. Learn. Sci. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"106508","DOI":"10.1016\/j.neunet.2024.106508","article-title":"Gradient-based optimization for quantum architecture search","volume":"179","author":"He","year":"2024","journal-title":"Neural Netw."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"032403","DOI":"10.1103\/PhysRevA.111.032403","article-title":"Self-supervised representation learning for Bayesian quantum architecture search","volume":"111","author":"He","year":"2025","journal-title":"Phys. Rev. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"045023","DOI":"10.1088\/2058-9565\/ac87cd","article-title":"Differentiable quantum architecture search","volume":"7","author":"Zhang","year":"2022","journal-title":"Quantum Sci. Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42484-025-00264-6","article-title":"Application of ZX-calculus to quantum architecture search","volume":"7","author":"Ewen","year":"2025","journal-title":"Quantum Mach. Intell."},{"key":"ref_40","unstructured":"Xie, S., Sarkar, A., and Feld, S. (2025). DeQompile: Quantum circuit decompilation using genetic programming for explainable quantum architecture search. arXiv."},{"key":"ref_41","unstructured":"Zhu, C., Wu, X., Zhang, H.K., Wu, S., Li, G., and Wang, X. (2025). Scalable Quantum Architecture Search via Landscape Analysis. arXiv."},{"key":"ref_42","unstructured":"F\u00f6sel, T., Niu, M.Y., Marquardt, F., and Li, L. (2021). Quantum circuit optimization with deep reinforcement learning. arXiv."},{"key":"ref_43","unstructured":"Kundu, A. (2024). Reinforcement learning-assisted quantum architecture search for variational quantum algorithms. arXiv."},{"key":"ref_44","unstructured":"Patel, Y.J., Kundu, A., Ostaszewski, M., Bonet-Monroig, X., Dunjko, V., and Danaci, O. (2024). Curriculum reinforcement learning for quantum architecture search under hardware errors. arXiv."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"025066","DOI":"10.1088\/2632-2153\/ade361","article-title":"Improving thermal state preparation of Sachdev\u2013Ye\u2013Kitaev model with reinforcement learning on quantum hardware","volume":"6","author":"Kundu","year":"2025","journal-title":"Mach. Learn. Sci. Technol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2100134","DOI":"10.1002\/qute.202100134","article-title":"Quantum Architecture Search with Meta-Learning","volume":"5","author":"He","year":"2022","journal-title":"Adv. Quantum Technol."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Pirhooshyaran, M., and Terlaky, T. (2021). Quantum Circuit Design Search. arXiv.","DOI":"10.1007\/s42484-021-00051-z"},{"key":"ref_48","unstructured":"Chen, C., He, Z., Zheng, S., Zhou, Y., and Situ, H. (2022). Fast optimal structures generator for parameterized quantum circuits. arXiv."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1038\/s42256-024-00831-9","article-title":"Quantum circuit synthesis with diffusion models","volume":"6","author":"Briegel","year":"2024","journal-title":"Nat. Mach. Intell."},{"key":"ref_50","first-page":"471","article-title":"EQNAS: Evolutionary Quantum Neural Architecture Search for Image Classification","volume":"168","author":"Li","year":"2023","journal-title":"Neural Netw. Off. J. Int. Neural Netw. Soc."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s12293-024-00417-3","article-title":"QEA-QCNN: Optimization of quantum convolutional neural network architecture based on quantum evolution","volume":"16","author":"Li","year":"2024","journal-title":"Memetic Comput."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2875","DOI":"10.1007\/s10773-014-2085-x","article-title":"Three Solvable Matrix Models of a Quantum Catastrophe","volume":"53","author":"Znojil","year":"2014","journal-title":"Int. J. Theor. Phys."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Znojil, M. (2022). Confluences of exceptional points and a systematic classification of quantum catastrophes. Sci. Rep., 12.","DOI":"10.1038\/s41598-022-07345-7"},{"key":"ref_54","unstructured":"Farhi, E., and Neven, H. (2018). Classification with Quantum Neural Networks on Near Term Processors. arXiv."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.neucom.2022.06.010","article-title":"Development of variational quantum deep neural networks for image recognition","volume":"501","author":"Wang","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1900070","DOI":"10.1002\/qute.201900070","article-title":"Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum-Classical Algorithms","volume":"2","author":"Sim","year":"2019","journal-title":"Adv. Quantum Technol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/733\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:06:29Z","timestamp":1760033189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/733"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,8]]},"references-count":56,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["e27070733"],"URL":"https:\/\/doi.org\/10.3390\/e27070733","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,8]]}}}