Abstract
For adaptive artificial intelligence systems, the question of the possibility of online learning is especially important, since such training provides adaptation. The purpose of the work is to consider methods of quantum machine online learning for the two most common architectures of quantum neural networks: feedforward and recurrent. The work uses the quantumz module available on PyPI to emulate quantum computing and create artificial quantum neural networks. In addition, the genser module is used to transform data dimensions, which provides reversible transformation of dimensions without loss of information. The data for the experiments are taken from open sources. The paper implements the machine learning method without optimization, proposed by the author earlier. Online learning algorithms for recurrent and feedforward quantum neural network are presented and experimentally confirmed. The proposed learning algorithms can be used as data science tools, as well as a part of adaptive intelligent control systems. The developed software can fully unleash its potential only on quantum computers, but, in the case of a small number of quantum registers, it can also be used in systems that emulate quantum computing, or in photonic computers.
Notes
In fact, there are some limitations, but they can be overcome by changing the attribute value ranges.
https://www.kaggle.com/datasets/jimschacko/airlines-dataset-to-predict-a-delay. Cited August 13, 2023.
REFERENCES
F. Tacchino, C. Macchiavello, D. Gerace, et al., “An artificial neuron implemented on an actual quantum processor,” npj Quantum Inf. 5 (1), 26 (2019).
T. Menneer and A. Narayanan, “Quantum-inspired neural networks,” in Proceedings of the Neural Information Processing Systems 95, Denver, CO, USA, November 27–30, 1995.
S. M. Gushanskii and V. E. Buglov, “Quantum deep learning of convolutional neural networks with the use of a variational quantum scheme,” Izv. Yuzhn. Fed. Univ. Tekh. Nauki 7 (224), 167–174 (2021).
I. Cong, S. Choi, and M. D. Lukin, “Quantum convolutional neural networks,” Nat. Phys. 15, 1273–1278 (2019).
I. Kerenidis, J. Landman, and A. Prakash, “Quantum algorithms for deep convolutional neural networks” (2019). https://doi.org/10.48550/arXiv.1911.01117
M. Henderson, S. Shakya, S. Pradhan, and T. Cook, “Quanvolutional neural networks: Powering image recognition with quantum circuits,” Quantum Mach. Intell. 2, 2 (2020).
P. Rebentrost, M. Mohseni, and S. Lloyd, “Quantum support vector machine for big data classification,” Phys. Rev. Lett. 113, 130503 (2014).
A. W. Harrow, A. Hassidim, and S. Lloyd, “Quantum algorithm for linear systems of equations,” Phys. Rev. Lett. 103, 150502 (2009).
Y. Dang, N. Jiang, H. Hu, Z. Ji, and W. Zhang, “Image classification based on quantum K-Nearest-Neighbor algorithm,” Quantum Inf. Process. 17, 1–18 (2018).
M. Schuld, I. Sinayskiy, and F. Petruccione, “Prediction by linear regression on a quantum computer,” Phys. Rev. A 94, 022342 (2016).
S. Lu and S. L. Braunstein, “Quantum decision tree classifier,” Quantum Inf. Process. 13, 757–770 (2014).
S. Lloyd, M. Mohseni, and P. Rebentrost, “Quantum algorithms for supervised and unsupervised machine learning” (2013). https://doi.org/10.48550/arXiv.1307.0411
S. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory 28, 129–137 (1982).
I. Kerenidis, J. Landman, A. Luongo, and A. Prakash, “q-means: A quantum algorithm for unsupervised machine learning” (2018). https://doi.org/10.48550/arXiv.1812.03584
E. Aïmeur, G. Brassard, and S. Gambs, “Quantum speed-up for unsupervised learning,” Mach. Learn. 90, 261–287 (2013).
D. P. DiVincenzo, “The physical implementation of quantum computation,” Fortschr. Phys. 48 (9–11), 771–783 (2000).
S. Lloyd, M. Mohseni, and P. Rebentrost, “Quantum principal component analysis,” Nat. Phys. 10, 631–633 (2014).
S. V. Zuev, “Geometric properties of quantum entanglement and machine learning,” Russ. Technol. J. 11 (5), 19–33 (2023).
P. D. Bruza and R. J. Cole, “Quantum logic of semantic space: An exploratory investigation of context effects in practical reasoning” (2006). https://arXiv:quant-ph/0612178. Accessed August 20, 2023.
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The work was carried out within the framework of the Priority-2030 development program on the material base of the Center for High Technologies of the Shukhov Belgorod State Technological University.
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Zuev, S.V. Statistical Online Learning in Recurrent and Feedforward Quantum Neural Networks. Dokl. Math. 108 (Suppl 2), S317–S324 (2023). https://doi.org/10.1134/S1064562423701557
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DOI: https://doi.org/10.1134/S1064562423701557