  Robust control design for quantum systems has been recognized as a key task
in quantum information technology, molecular chemistry and atomic physics. In
this paper, an improved differential evolution algorithm, referred to as
\emph{msMS}\_DE, is proposed to search robust fields for various quantum
control problems. In \emph{msMS}\_DE, multiple samples are used for fitness
evaluation and a mixed strategy is employed for the mutation operation. In
particular, the \emph{msMS}\_DE algorithm is applied to the control problems of
(i) open inhomogeneous quantum ensembles and (ii) the consensus goal of a
quantum network with uncertainties. Numerical results are presented to
demonstrate the excellent performance of the improved machine learning
algorithm for these two classes of quantum robust control problems.
Furthermore, \emph{msMS}\_DE is experimentally implemented on femtosecond laser
control applications to optimize two-photon absorption and control
fragmentation of the molecule $\text{CH}_2\text{BrI}$. Experimental results
demonstrate excellent performance of \emph{msMS}\_DE in searching for effective
femtosecond laser pulses for various tasks.
