Data-driven modeling and control of quantum dynamics

Abstract

Control is the factor that delineates quantum science from quantum engineering. Model-based optimal control is a modern approach to practical control engineering. It designs control laws using optimization based on dynamical models of the system. If models are perfect, then successful control is realized by simply applying optimal control using the ideal predictions as needed. However, when models aren't perfect, directly applying optimal control produces undesired outcomes due to inaccurate predictions. In this case, we must turn to data-driven methods to improve modeling or control design. This thesis explores two novel ways to incorporate data to control quantum systems that are imperfectly modeled. First, we pursue data-driven modeling, and introduce a physics-informed regression-based approach to learn a model for the quantum control dynamics directly from time series measurements. Second, we pursue data-driven control design, and apply model predictive control to synthesize optimal controls for robust quantum state preparation. In addition to these two novel results, the necessary background in quantum mechanics is provided. Also, data-driven modeling and optimal control are reviewed and contextualized within quantum optimal control. We conclude by offering our perspective on future directions for data-driven approaches to model-based quantum optimal control.