Optimal probabilistic quantum control theory

Abstract: There is a fundamental limit to what is knowable about atomic and molecular scale systems. This fuzziness is not always due to the act of measurement. Other contributing factors include system parameter uncertainty, functional uncertainty that originates from input functions, and sensors noises to mention a few. This indeterminism has led to major challenges in the development of accurate control methods for atomic scale systems. To address the probabilistic and uncertain nature of these systems, this work proposes a novel control framework that considers the representation of the system quantum states and the quantification of its physical properties following a probabilistic approach. Our framework is fully probabilistic. It uses the Shannon relative entropy from information theory to design optimal randomised controllers that can achieve a desired outcome of an atomic scale system. Several experiments are carried out to illustrate the applicability and effectiveness of the proposed approach.