  In this paper, we propose a scheme to eliminate the influence of noises on
system dynamics, by means of a sequential unsharp measurements and unitary
feedback operations. The unsharp measurements are carried out periodically
during system evolution, while the feedback operations are well designed based
on the eigenstates of the density matrices of the exact (noiseless) dynamical
states and its corresponding post-measurement states. For illustrative
examples, we show that the dynamical trajectory errors caused by both static
and non-static noises are successfully eliminated in typical two-level and
multi-level systems, i.e., the high-fidelity quantum dynamics can be
maintained. Furthermore, we discuss the influence of noise strength and
measurement strength on the degree of precise quantum control. Crucially, the
measurement-feedback scheme is quite universal in that it can be applied to
precise quantum control for any dimension systems. Thus, it naturally finds
extensive applications in quantum information processing.
