Characterization and Control of Quantum Dynamics: Computational Methodology Developments and NMR Demonstrations

Abstract

Characterization and control in quantum dynamics are paramount for the emerging field of quantum technologies. In the realm of quantum mechanics, the Schrödinger equation or Von-Neumann equation governs quantum evolution. However, efficiently characterizing the final state and determining external parameters or controls remains challenging, necessitating the development of advanced computational methodologies. This thesis focuses on developing and demonstrating innovative computational approaches for efficient characterization and control of quantum dynamics. The first key aspect involves the application of a machine-learning algorithm known as the recommender system (RS). In this context, RS is utilized to estimate changes in quantum correlations following unitary or nonunitary evolution. Remarkably, RS demonstrates the capability to estimate quantities that are challenging to compute or lack analytical expressions. The subsequent discussion revolves around three distinct developments within the control framework and their demonstration using Nuclear Magnetic Resonance (NMR) experiments. Firstly, the thesis delves into RS-expedited quantum control optimization, where the machine learning algorithm efficiently populates a sparse table of quantum controls. Secondly, the concept of ‘push-pull quantum control’ is introduced, leveraging a target operator alongside a set of orthogonal operators to generate robust control sequences effectively. Lastly, implementing a Physics-informed neural network for solving the time-dependent Schrödinger equation is explained, highlighting its advantages, particularly avoiding prior discretization of the parameter space. These methodologies are demonstrated to be versatile and applicable across different physical hardware, signifying their crucial role in the unfolding landscape of quantum technologies.