Redes neurais clássicas e quânticas

Abstract

This Ph.D. Thesis is dedicated to the integrated study of classical and quantum neural networks applied to physical systems, with emphasis on continuous-variable quantum computing (CVQC), physics-informed inverse problems, and second-order neurons with mixed functions for solving differential equations. The investigation is structured into four parts and demonstrates: the feasibility of QNNs in CVQC for regression tasks; the robustness of the PINNverse method for parameter inference in open systems; and the gains in accuracy and interpretability provided by mixed-function neurons, which enable parsimonious functional compositions. In the numerical results, the application of quantum neural networks to regression problems stands out, achieving errors on the order of 10−5. When comparing quantum and classical neural networks, an advantage was observed for the quantum case in obtaining solutions for sinusoidal functions, depending on the comparison criteria and the hyperparameters defined for the classical network. The PINNverse method demonstrated the ability to recover Hamiltonian parameters and dissipative rates with high precision, even in the presence of simulated noisy data. When applied to experimental data, the method showed excellent agreement with values reported in the literature, achieving errors smaller than those of the comparative models. Finally, in the MixFunn and Mix2Funn architectures, the model achieved low errors between analytical and simulated solutions, while also being capable of extracting the analytical expression itself. Another relevant result was the advantage in the number of parameters required to solve the differential equations, evidencing the structural efficiency of the proposed model.