Title:  From Randomized Fourier Neural Networks to Quantum Computing and Digital Twins

Abstract:  In this talk, I will provide an overview of my current research, which spans neural networks and quantum computing. The first part will introduce a new class of neural networks called random residual Fourier networks, designed to enable deep learning through optimal sampling techniques. I will present both theoretical insights and numerical results to demonstrate the advantages of this approach. In the second part, I will shift focus to quantum computing, with an emphasis on quantum characterization and optimal control. I will introduce a novel framework for quantum characterization and control that combines optimal transportation theory with generalized Bayesian inference, offering enhanced uncertainty quantification of quantum systems and robust quantum gate design. I conclude with a brief research plan toward the development of quantum digital twins.