Controlling the probability density of quantum systems

A new method to design a quantum controller which directly controls the probability density function (PDF) of quantum systems is proposed. Based on the quantum model from the PDF perspective, two specific control algorithms are proposed with uniform and non-uniform fields, respectively. Then a detailed control algorithm with convergence analysis is given for the small error case. By appropriately estimating the selected Lyapunov function, more accurate control effect is achieved. The proposed scheme provides a constructive method to find appropriate parameters for controller design.