Comparison of classical machine learning approaches with hybrid quantum approaches in applied problems

The work is aimed at analyzing the potential advantages of using quantum approaches in applied problems of artificial intelligence. In this paper, the task of classifying medical images extracted from histopathological images of sections of lymph nodes is set. The theoretical basis used for the construction of quantum and hybrid-quantum computing elements used in the article will be given. Quantum analogues of classical machine learning algorithms and neural networks will be considered. The paper will give a step-by-step description of the data transformation, the construction of models and their training, followed by an analysis of the results obtained and the performance of the simulation of quantum computing.

1. Nielsen M.A, Chuang I.L., Quantum Computing and Quantum Information, Cabridge, 2010, ISBN: 9781107002173, DOI: https://doi.org/10.1017/CBO9780511976667, pp. 702.
2. PCAM Dataset. Github, Available at: https://github.com/basveeling/pcam
3. Aer quantum simulator. Qiskit Documentation. IBM, Available at: https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.AerSimulator.html
4. Akhmed S.K. Source code of experiments. Github, Available at: https://github.com/Untronix0nly/Quantum-Hybrid-Machine-Learning
5. Sukin Sim, Peter D. Johnson and Alan Aspuru-Guzik, Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms, Advanced Quantum Technology 2 (2019) 1900070, doi:10.1002/qute.201900070, arXiv:1905.10876.
6. Vojtech Havlicek, Antonio D. Córcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow and Jay M. Gambetta, Supervised learning with quantum enhanced feature spaces, Nature 567, 209-212 (2019), doi.org:10.1038/s41586-019-0980-2, arXiv:1804.11326.
7. Jennifer R. Glick, Tanvi P. Gujarati, Antonio D. Corcoles, Youngseok Kim, Abhinav Kandala, Jay M. Gambetta, Kristan Temme, Covariant quantum kernels for data with group structure, doi: 48550/arXiv.2105.03406, arXiv: 2105.03406v2
8. Spall, J. C., “A Stochastic Approximation Technique for Generating Maximum Likelihood Parameter Estimates,” Proceedings of the American Control Conference, Minneapolis, MN, June 1987, pp. 1161–1167.
9. Spall, J. C.,“Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation,” IEEE Transactions on Automatic Control, vol. 37(3), pp. 332–341.
10. Spall, J.C., "Overview of the Simultaneous Perturbation Method for Efficient Optimization" 2. Johns Hopkins APL Technical Digest, 19(4), 482–492.
11. J. D. Powell, "A direct search optimization method that models the objective and constraint functions by linear interpolation," in Advances in Optimization and Numerical Analysis, eds. S. Gomez and J.-P. Hennart (Kluwer Academic: Dordrecht, 1994), p. 51-67.
12. S. Veeling, J. Linmans, J. Winkens, T. Cohen, M. Welling. "Rotation Equivariant CNNs for Digital Pathology". arXiv:1806.03962