From certainty to chance: probabilistic insights into quantum control

Abstract This study introduces an innovative control methodology designed specifically for quantum physical systems. It bridges a critical gap by accounting for the full spectrum of uncertainties and noise that could affect the time evolution of these systems. In contrast to conventional methods, our pioneering approach utilizes probability density functions (pdfs) to characterize quantum dynamics, providing a more detailed and accurate description of their temporal behavior. We propose a strategy that seeks to minimize the discrepancy between the actual pdf, which encapsulates the combined dynamics of the quantum system and an external electric field, and a desired pdf that aligns with the system’s intended outcomes. This strategy marks a significant shift from traditional quantum control techniques. Initially, we present a solution for controlling quantum systems defined by general pdfs. This solution is then demonstrated on quantum systems described by Gaussian pdfs, with an in-depth account of the resulting optimized controller’s structure. The study culminates with practical demonstrations, showcasing the approach’s efficacy and practicality, thus endorsing its potential as a formidable instrument in quantum control. Graphical abstract