References
- Al-Khafaji, M. and Ramaha, N. (2025). Hybrid deep learning architecture for scalable and high-quality image compression, Scientific Reports 15(1): 22926, DOI: 10.1038/s41598-025-06481-0.
- Aslam, M.M., Tufail, A., Silva, L.C.D., Apong, R.A.A.H.M. and Namoun, A. (2024). An improved autoencoder-based approach for anomaly detection in industrial control systems, Systems Science & Control Engineering 12(1): 2334303, DOI: 10.1080/21642583.2024.2334303.
- Baldi, P. and Hornik, K. (1989). Neural networks and principal component analysis: Learning from examples without local minima, Neural Networks 2(1): 53–58, DOI: 10.1016/0893-6080(89)90014-2.
- Bravo-Prieto, C. (2021). Quantum autoencoders with enhanced data encoding, Machine Learning: Science and Technology 2(3): 035028, DOI: 10.1088/2632-2153/ac0616.
- Brooks, M. (2019). Beyond quantum supremacy: The hunt for useful quantum computers, Nature 574(7776): 19–21, DOI: 10.1038/d41586-019-02936-3.
- Cao, C. and Wang, X. (2021). Noise-assisted quantum autoencoder, Physical Review Applied 15(5): 054012, DOI: 10.1103/PhysRevApplied.15.054012.
- Ciliberto, C., Herbster, M., Ialongo, A.D., Pontil, M., Rocchetto, A., Severini, S. and Wossnig, L. (2018). Quantum machine learning: A classical perspective, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474(2209): 20170551, DOI: 10.1098/rspa.2017.0551.
- Cong, I., Choi, S. and Lukin, M.D. (2019). Quantum convolutional neural networks, Nature Physics 15(12): 1273–1278, DOI: 10.1038/s41567-019-0648-8.
- Cottrell, G.W., Munro, P. and Zipser, D. (1987). Learning internal representation from gray-scale images: An example of extensional programming, Proceedings of the 9th Annual Meeting of the Cognitive Science Society, Seattle, USA, pp. 462–473.
- Devlin, J., Chang, M., Lee, K. and Toutanova, K. (2018). BERT: Pre-training of deep bidirectional transformers for language understanding, CoRR abs/1810.04805.
- Du, Y. and Tao, D. (2025). On exploring the potential of quantum auto-encoder for learning quantum systems, IEEE Transactions on Neural Networks and Learning Systems 36(7): 12454–12468, DOI: 10.1109/TNNLS.2024.3474793.
- Fournier, Q. and Aloise, D. (2019). Empirical comparison between autoencoders and traditional dimensionality reduction methods, Proceedings of the IEEE 2nd International Conference on Artificial Intelligence and Knowledge Engineering (AIKE), Los Alamitos, USA, pp. 211–214, DOI: 10.1109/AIKE.2019.00044.
- He, K., Chen, X., Xie, S., Li, Y., Dollár, P. and Girshick, R. (2022). Masked autoencoders are scalable vision learners, Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, USA, pp. 15979–15988, DOI: 10.1109/CVPR52688.2022.01553.
- Higgins, I., Matthey, L., Pal, A., Burgess, C.P., Glorot, X., Botvinick, M. M., Mohamed, S. and Lerchner, A. (2017). β-VAE: Learning basic visual concepts with a constrained variational framework, Proceedings of the 5th International Conference on Learning Representations, ICLR 2017, Toulon, France.
- Hinton, G.E. and Salakhutdinov, R. (2006). Reducing the dimensionality of data with neural networks, Science 313(5786): 504–507, DOI: 10.1126/science.1127647.
- Hirvensalo, M. (2004). Quantum Computing, 2nd Edn, Springer, Berlin/Heidelberg, DOI: 0.1007/978-3-662-09636-9.
- Huang, H.-Y., Broughton, M., Mohseni, M., Babbush, R., Boixo, S., Neven, H. and McClean, J.R. (2021). Power of data in quantum machine learning, Nature Communications 12(1): 2631, DOI: 10.1038/s41467-021-22539-9.
- Janjua, J. and Patankar, A. (2024). Exploring the impact of denoising autoencoder architectures on image retrieval, Procedia Computer Science 235: 2557–2566, DOI: 10.1016/j.procs.2024.04.241.
- Kingma, D.P. and Welling, M. (2014). Auto-encoding variational Bayes, Proceedings of the 2nd International Conference on Learning Representations, ICLR 2014, Banff, Canada.
- Kramer, M.A. (1991). Nonlinear principal component analysis using autoassociative neural networks, AIChE Journal 37(2): 233–243, DOI: 10.1002/aic.690370209.
- Kramer, M.A. (1992). Autoassociative neural networks, Computers & Chemical Engineering 16(4): 313–328, DOI: 10.1016/0098-1354(92)80051-A.
- Kurowski, K., Slysz, M., Subocz, M. and Rózycki, R. (2021). Applying a quantum, annealing based restricted Boltzmann machine for MNIST handwritten digit classification, Computational Methods in Science and Technology 27(3): 99–107, DOI: 10.12921/cmst.2021.0000011.
- Le, Q.V., Ranzato, M., Monga, R., Devin, M., Chen, K., Corrado, G.S., Dean, J. and Ng, A.Y. (2012). Building high-level features using large scale unsupervised learning, Proceedings of the 29th International Conference on Machine Learning, ICML’12, Madison, USA, p. 507–514.
- Liu, Z., Kalogeiton, V. and Cani, M. (2021). Multiple style transfer via variational autoencoder, Proceedings of the IEEE International Conference on Image Processing, ICIP 2021, Anchorage, USA, pp. 2413–2417, DOI: 10.1109/ICIP42928.2021.9506379.
- Loey, M., El-Sawy, A. and El-Bakry, H.M. (2017). Deep learning autoencoder approach for handwritten Arabic digits recognition, CoRR abs/1706.06720, DOI: 10.48550/arXiv.1706.06720.
- Luhman, T. and Luhman, E. (2023). High fidelity image synthesis with deep VAEs in latent space, CoRR abs/2303.13714, DOI: 10.48550/ARXIV.2303.13714.
- Ma, H., Huang, C.-J., Chen, C., Dong, D., Wang, Y., Wu, R.-B. and Xiang, G.-Y. (2023). On compression rate of quantum autoencoders: Control design, numerical and experimental realization, Automatica 147: 110659, DOI: 10.1016/j.automatica.2022.110659.
- Makhzani, A., Shlens, J., Jaitly, N. and Goodfellow, I.J. (2015). Adversarial autoencoders, CoRR abs/1511.05644, DOI: 10.48550/arXiv.1511.05644.
- Mangini, S., Marruzzo, A., Piantanida, M., Gerace, D., Bajoni, D. and Macchiavello, C. (2022). Quantum neural network autoencoder and classifier applied to an industrial case study, Quantum Machine Intelligence 4(2): 13, DOI: 10.1007/s42484-022-00070-4.
- Masci, J., Meier, U., Cireşan, D. and Schmidhuber, J. (2011). Stacked convolutional auto-encoders for hierarchical feature extraction, in T. Honkela et al. (Eds), Artificial Neural Networks and Machine Learning, ICANN 2011, Springer, Berlin/Heidelberg, pp. 52–59, DOI: 10.1007/978-3-642-21735-7_7.
- Neloy, A.A. and Turgeon, M. (2024). A comprehensive study of auto-encoders for anomaly detection: Efficiency and trade-offs, Machine Learning with Applications 17: 100572, DOI: 10.1016/j.mlwa.2024.100572.
- Nielsen, M.A. and Chuang, I.L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition, Cambridge University Press, Cambridge.
- Parthasarathy, K. (1992). An Introduction to Quantum Stochastic Calculus, Birkhäuser, Basel, DOI: 10.1007/978-3-0348-0566-7.
- Powell, M.J.D. (1994). A direct search optimization method that models the objective and constraint functions by linear interpolation, in S. Gomez and J.P. Hennart (Eds), Advances in Optimization and Numerical Analysis, Mathematics and Its Applications, Vol. 275, Springer Netherlands, Dordrecht, pp. 51–67, DOI: 10.1007/978-94-015-8330-5_4.
- Powell, M.J.D. (2007). A view of algorithms for optimization without derivatives, Technical report, DAMTP 2007/NAO3, Cambridge University, Cambridge.
- Preskill, J. (2018). Quantum computing in the NISQ era and beyond, Quantum 2: 79, DOI: 10.22331/q-2018-08-06-79.
- Ritter, M.B. (2019). Near-term quantum algorithms for quantum many-body systems, Journal of Physics: Conference Series 1290(1): 012003, DOI: 10.1088/1742-6596/1290/1/012003.
- Romero, J., Olson, J.P. and Aspuru-Guzik, A. (2017). Quantum autoencoders for efficient compression of quantum data, Quantum Science and Technology 2(4): 045001, DOI: 10.1088/2058-9565/aa8072.
- Sawerwain, M. and Kowal, M. (2025a). Github repository for the PolLettDS dataset, https://github.com/qMSUZ/PolLettDS.
- Sawerwain, M. and Kowal, M. (2025b). Source code of examples of a quantum autoencoder, https://github.com/qMSUZ/QAutoEnc.
- Shang, W., Qiu, J., Shi, H., Wang, S., Ding, L. and Xiao, Y. (2024). An efficient anomaly detection method for industrial control systems: Deep convolutional autoencoding transformer network, International Journal of Intelligent Systems 2024(1): 5459452, DOI: 10.1155/2024/5459452.
- Sivarajah, S., Dilkes, S., Cowtan, A., Simmons, W., Edgington, A. and Duncan, R. (2020). t|ket〉: A retargetable compiler for NISQ devices, Quantum Science and Technology 6(1): 014003, DOI: 10.1088/2058-9565/ab8e92.
- Slysz, M., Kurowski, K., Waligóra, G. and Węglarz, J. (2023). Exploring the capabilities of quantum support vector machines for image classification on the mnist benchmark, in J. Mikyška et al. (Eds), Computational Science, ICCS 2023, Springer Nature Switzerland, Cham, pp. 193–200, DOI: 10.1007/978-3-031-36030-5_15.
- Tokovarov, M., Kaczorowska, M. and Milosz, M. (2020). Development of extensive Polish handwritten characters database for text recognition research, Advances in Science and Technology Research Journal 14(3): 30–38, DOI: 10.12913/22998624/122567.
- Vincent, P., Larochelle, H., Bengio, Y. and Manzagol, P.-A. (2008). Extracting and composing robust features with denoising autoencoders, Proceedings of the 25th International Conference on Machine Learning, ICML’08, New York, USA, pp. 1096–1103, DOI: 10.1145/1390156.1390294.
- Vincent, P., Larochelle, H., Lajoie, I., Bengio, Y. and Manzagol, P.-A. (2010). Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion, Journal of Machine Learning Research 11: 3371–3408.
- Wang, H., Tan, J., Huang, Y. and Zheng, W. (2024). Quantum image compression with autoencoders based on parameterized quantum circuits, Quantum Information Processing 23(2): 41, DOI: 10.1007/s11128-023-04243-3.
- Weigold, M., Barzen, J., Leymann, F. and Salm, M. (2021). Expanding data encoding patterns for quantum algorithms, Proceedings of the IEEE 18th International Conference on Software Architecture Companion (ICSA-C), Stuttgart, Germany, pp. 95–101, DOI: 10.1109/ICSA-C52384.2021.00025.
- Wu, J., Fu, H., Zhu, M., Zhang, H., Xie, W. and Li, X.-Y. (2024). Quantum circuit autoencoder, Physical Review A 109(3): 032623, DOI: 10.1103/PhysRevA.109.032623.
- Zeguendry, A., Jarir, Z. and Quafafou, M. (2023). Quantum machine learning: A review and case studies, Entropy 25(2): 287, DOI: 10.3390/e25020287.