Methods for Quantum Dynamics,Localization and Quantum MachineLearning

The thesis is divided into three parts. In the first part, we explore scenarios where quantum dynamics is slow and information is localized. In the second part, we design thermodynamic protocols by engineering time-dependent Hamiltonians of a system interacting with its bath. Finally, in the third part, we examine the intersections between tensor-network methods for quantum mechanics and machine learning methods.