Pulse controlled non-adiabatic quantum state transmission (QST) was proposed
many years ago. However, in practice environmental noise inevitably damages
communication quality in the proposal. In this paper, we study the optimally
controlled non-adiabatic QST in the presence of quantum noise. By using the
Adam algorithm, we find that the optimal pulse sequence can dramatically
enhance the transmission fidelity of such an open system. In comparison with
the idealized pulse sequence in a closed system, it is interesting to note that
the improvement of the fidelity obtained by the Adam algorithm can even be
better for a bath strongly coupled to the system. Furthermore, we find that the
Adam algorithm remains powerful for different number of sites and different
types of Lindblad operators, showing its universality in performing optimal
control of quantum information processing tasks
