  A new control method that considers all sources of uncertainty and noises
that might affect the time evolutions of quantum physical systems is
introduced. Under the proposed approach, the dynamics of quantum systems are
characterised by probability density functions (pdfs), thus providing a
complete description of their time evolution. Using this probabilistic
description, the proposed method suggests the minimisation of the distance
between the actual pdf that describes the joint distribution of the time
evolution of the quantum system and the external electric field, and the
desired pdf that describes the system target outcome. We start by providing the
control solution for quantum systems that are characterised by arbitrary pdfs.
The obtained solution is then applied to quantum physical systems characterised
by Gaussian pdfs and the form of the optimised controller is elaborated.
Finally, the proposed approach is demonstrated on a real molecular system and
two spin systems showing the effectiveness and simplicity of the method.
