ON THEORETICAL ANALYSES OF QUANTUM SYSTEMS: PHYSICS AND MACHINE LEARNING

Engineered quantum systems can help us learn more about fundamental physics topics and quantum technologies with real-world applications. However, building them could involve several challenging tasks, such as designing more noise-resistant quantum components in confined space, manipulating continuously-measured quantum systems without destroying coherence, and extracting information about quantum phenomena using machine learning (ML) tools. In this dissertation, we present three examples from the three aspects of studying the dynamics and characteristics of various quantum systems. First, we examine a circuit quantum acoustodynamic system consisting of a superconducting qubit, an acoustical waveguide, and a transducer that nonlocally couples both. As the sound signals travel $10^5$ times slower than the light and the coupler dimension extends beyond a few phonon emission wavelengths, we can model the system as a non-Markovian giant atom. With an explicit result, we show that a giant atom can exhibit suppressed relaxation within a free space and an effective vacuum coupling emerges between the qubit excitation and a confined acoustical wave packet. Second, we study closed-loop controls for open quantum systems using weakly-monitored Bose-Einstein condensates (BECs) as a platform. We formulate an analytical model to describe the dynamics of backaction-limited weak measurements and temporal-spatially resolved feedback imprinting. Furthermore, we design a backaction-heating-prevention feedback protocol that stabilizes the system in quasi-equilibrium. With these results, we introduce closed-loop control as a powerful instrument for engineering open quantum systems. At last, we establish an automated framework consisting of ML and physics-informed models for solitonic feature identification from experimental BEC image data. We develop classification and object detection algorithms based on convolutional neural networks. Our framework eliminates human inspections and enables studying soliton dynamics from numerous images. Moreover, we publish a labeled dataset of soliton images and an open-source Python package for implementing our framework