Quantum Neural Networks: Advantages in Processing High-Dimensional Hilbert Space Data
Abstract
Quantum machine learning has emerged as a promising paradigm for addressing the limitations of classical learning models in handling data with exponentially growing dimensionality. In particular, many problems in physics, chemistry, and quantum information are naturally represented in high-dimensional Hilbert spaces, where classical neural networks face significant challenges related to representation efficiency and scalability. This study aims to analyze the advantages of quantum neural networks in processing data embedded in high-dimensional Hilbert spaces and to clarify the structural sources of their potential superiority over classical architectures. The research adopts a theoretical–computational approach that combines analytical modeling with numerical simulations of variational quantum circuits and comparable classical neural network models across increasing dimensional regimes. Performance is evaluated in terms of learning fidelity, parameter scaling behavior, and stability under dimensional growth. The results show that quantum neural networks consistently maintain higher fidelity with substantially fewer parameters as Hilbert space dimensionality increases, while classical models exhibit rapid performance degradation and escalating complexity. These findings indicate that quantum neural networks benefit from intrinsic alignment with Hilbert space geometry through superposition and entanglement. In conclusion, the study demonstrates that quantum neural networks constitute a distinct and scalable learning framework for high-dimensional data, supporting their relevance for future quantum-enhanced machine learning applications..
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References
Aliabadi, F. (2022). Chaos synchronization using adaptive quantum neural networks and its application in secure communication and cryptography. Neural Computing and Applications, 34(8), 6521–6533. https://doi.org/10.1007/s00521-021-06768-z
Barrett, T. D. (2022). Autoregressive neural-network wavefunctions for ab initio quantum chemistry. Nature Machine Intelligence, 4(4), 351–358. https://doi.org/10.1038/s42256-022-00461-z
Bikku, T. (2024). A Novel Quantum Neural Network Approach to Combating Fake Reviews. International Journal of Networked and Distributed Computing, 12(2), 195–205. https://doi.org/10.1007/s44227-024-00028-x
Di, S. (2023). Amplitude transformed quantum convolutional neural network. Applied Intelligence, 53(18), 20863–20873. https://doi.org/10.1007/s10489-023-04581-w
Domingo, L. (2023). Binding affinity predictions with hybrid quantum-classical convolutional neural networks. Scientific Reports, 13(1). https://doi.org/10.1038/s41598-023-45269-y
Dong, Y. (2023). An improved hybrid quantum-classical convolutional neural network for multi-class brain tumor MRI classification. Journal of Applied Physics, 133(6). https://doi.org/10.1063/5.0138021
Felefly, T. (2023). An Explainable MRI-Radiomic Quantum Neural Network to Differentiate Between Large Brain Metastases and High-Grade Glioma Using Quantum Annealing for Feature Selection. Journal of Digital Imaging, 36(6), 2335–2346. https://doi.org/10.1007/s10278-023-00886-x
Ghosh, N. (2023). An Evolving Quantum Fuzzy Neural Network for online State-of-Health estimation of Li-ion cell. Applied Soft Computing, 143(Query date: 2026-02-12 02:19:33). https://doi.org/10.1016/j.asoc.2023.110263
Girardin, A. (2022). Building separable approximations for quantum states via neural networks. Physical Review Research, 4(2). https://doi.org/10.1103/PhysRevResearch.4.023238
Gupta, I. (2024). A Multiple Controlled Toffoli Driven Adaptive Quantum Neural Network Model for Dynamic Workload Prediction in Cloud Environments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(12), 7574–7588. https://doi.org/10.1109/TPAMI.2024.3402061
Hermann, J. (2023). Ab initio quantum chemistry with neural-network wavefunctions. Nature Reviews Chemistry, 7(10), 692–709. https://doi.org/10.1038/s41570-023-00516-8
Hossain, S. (2024). A Deep Quantum Convolutional Neural Network Based Facial Expression Recognition For Mental Health Analysis. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 32(Query date: 2026-02-12 02:19:33), 1556–1565. https://doi.org/10.1109/TNSRE.2024.3385336
Hou, X. (2023). A duplication-free quantum neural network for universal approximation. Science China Physics Mechanics and Astronomy, 66(7). https://doi.org/10.1007/s11433-023-2098-8
Ibayashi, H. (2023). Allegro-Legato: Scalable, Fast, and Robust Neural-Network Quantum Molecular Dynamics via Sharpness-Aware Minimization. Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 13948(Query date: 2026-02-12 02:19:33), 223–239. https://doi.org/10.1007/978-3-031-32041-5_12
Karthick, G. S. (2023). Chronic obstructive pulmonary disease prediction using Internet of things-spiro system and fuzzy-based quantum neural network classifier. Theoretical Computer Science, 941(Query date: 2026-02-12 02:19:33), 55–76. https://doi.org/10.1016/j.tcs.2022.08.021
Kim, J. (2023). Classical-to-quantum convolutional neural network transfer learning. Neurocomputing, 555(Query date: 2026-02-12 02:19:33). https://doi.org/10.1016/j.neucom.2023.126643
Konar, D. (2023). A shallow hybrid classical–quantum spiking feedforward neural network for noise-robust image classification. Applied Soft Computing, 136(Query date: 2026-02-12 02:19:33). https://doi.org/10.1016/j.asoc.2023.110099
Kumar, J. (2023). A Quantum Controlled-NOT Neural Network-Based Load Forecast and Management Model for Smart Grid. IEEE Systems Journal, 17(4), 5714–5725. https://doi.org/10.1109/JSYST.2023.3309324
Liu, G. (2022). A quantum artificial neural network for stock closing price prediction. Information Sciences, 598(Query date: 2026-02-12 02:19:33), 75–85. https://doi.org/10.1016/j.ins.2022.03.064
Liu, J. (2023). Analytic Theory for the Dynamics of Wide Quantum Neural Networks. Physical Review Letters, 130(15). https://doi.org/10.1103/PhysRevLett.130.150601
Luo, D. (2022). Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation. Physical Review Letters, 128(9). https://doi.org/10.1103/PhysRevLett.128.090501
MacCormack, I. (2022). Branching quantum convolutional neural networks. Physical Review Research, 4(1). https://doi.org/10.1103/PhysRevResearch.4.013117
Massoli, F. V. (2023). A Leap among Quantum Computing and Quantum Neural Networks: A Survey. ACM Computing Surveys, 55(5). https://doi.org/10.1145/3529756
Mohan, M. (2023). Accurate prediction of carbon dioxide capture by deep eutectic solvents using quantum chemistry and a neural network. Green Chemistry, 25(9), 3475–3492. https://doi.org/10.1039/d2gc04425k
Nguyen, N. (2022). Bayesian Quantum Neural Networks. IEEE Access, 10(Query date: 2026-02-12 02:19:33), 54110–54122. https://doi.org/10.1109/ACCESS.2022.3168675
Nguyen, P. N. (2024). Biomarker discovery with quantum neural networks: A case-study in CTLA4-activation pathways. BMC Bioinformatics, 25(1). https://doi.org/10.1186/s12859-024-05755-0
Nguyen, T. (2022). An Evaluation of Hardware-Efficient Quantum Neural Networks for Image Data Classification. Electronics Switzerland, 11(3). https://doi.org/10.3390/electronics11030437
Pfau, D. (2024). Accurate computation of quantum excited states with neural networks. Science, 385(6711). https://doi.org/10.1126/science.adn0137
Pira, L. (2023). An invitation to distributed quantum neural networks. Quantum Machine Intelligence, 5(2). https://doi.org/10.1007/s42484-023-00114-3
Rende, R. (2024). A simple linear algebra identity to optimize large-scale neural network quantum states. Communications Physics, 7(1). https://doi.org/10.1038/s42005-024-01732-4
Riaz, F. (2023). Accurate Image Multi-Class Classification Neural Network Model with Quantum Entanglement Approach. Sensors, 23(5). https://doi.org/10.3390/s23052753
Shahwar, T. (2022). Automated Detection of Alzheimer’s via Hybrid Classical Quantum Neural Networks. Electronics Switzerland, 11(5). https://doi.org/10.3390/electronics11050721
Song, Y. (2024). A resource-efficient quantum convolutional neural network. Frontiers in Physics, 12(Query date: 2026-02-12 02:19:33). https://doi.org/10.3389/fphy.2024.1362690
Taheri-Garavand, A. (2022). Application of artificial neural networks for the prediction of performance and exhaust emissions in IC engine using biodiesel-diesel blends containing quantum dot based on carbon doped. Energy Conversion and Management X, 16(Query date: 2026-02-12 02:19:33). https://doi.org/10.1016/j.ecmx.2022.100304
Ullah, U. (2022). A Fully Connected Quantum Convolutional Neural Network for Classifying Ischemic Cardiopathy. IEEE Access, 10(Query date: 2026-02-12 02:19:33), 134592–134605. https://doi.org/10.1109/ACCESS.2022.3232307
Wei, S. J. (2022). A quantum convolutional neural network on NISQ devices. Aapps Bulletin, 32(1). https://doi.org/10.1007/s43673-021-00030-3
Yousif, M. (2024). A New Quantum Circuits of Quantum Convolutional Neural Network for X-Ray Images Classification. IEEE Access, 12(Query date: 2026-02-12 02:19:33), 65660–65671. https://doi.org/10.1109/ACCESS.2024.3396411
Yu, W. (2024). Application of Quantum Recurrent Neural Network in Low-Resource Language Text Classification. IEEE Transactions on Quantum Engineering, 5(Query date: 2026-02-12 02:19:33). https://doi.org/10.1109/TQE.2024.3373903
Zeng, Y. (2022). A Multi?Classification Hybrid Quantum Neural Network Using an All?Qubit Multi?Observable Measurement Strategy. Entropy, 24(3). https://doi.org/10.3390/e24030394
Zheng, J. (2025). A Quantum Spatial Graph Convolutional Neural Network Model on Quantum Circuits. IEEE Transactions on Neural Networks and Learning Systems, 36(3), 5706–5720. https://doi.org/10.1109/TNNLS.2024.3382174
Zhou, B. (2023). Accelerated Quantum Mechanics/Molecular Mechanics Simulations via Neural Networks Incorporated with Mechanical Embedding Scheme. Journal of Chemical Theory and Computation, 19(4), 1157–1169. https://doi.org/10.1021/acs.jctc.2c01131
Zhou, H. (2023). A self-organizing fuzzy neural network modeling approach using an adaptive quantum particle swarm optimization. Applied Intelligence, 53(11), 13569–13592. https://doi.org/10.1007/s10489-022-04133-8
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Copyright (c) 2026 Eka Utaminingsih, , Luca Santi, Sione Kakala
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