  In designing quantum control, it is generally required to simulate the
controlled system evolution with a classical computer. However, computing the
time evolution operator can be quite resource-consuming since the total
Hamiltonian is often hard to diagonalize. In this paper, we mitigate this issue
by substituting the time evolution segments with their Trotter decompositions,
which reduces the propagator into a combination of single-qubit operations and
fixed-time system evolutions. The resulting procedure can provide substantial
speed gain with acceptable costs in the propagator error. As a demonstration,
we apply the proposed strategy to improve the efficiency of the gradient ascent
pulse engineering algorithm for searching optimal control fields. Furthermore,
we show that the higher-order Trotter decompositions can provide efficient
Ans\"atze for the variational quantum algorithm, leading to improved
performance in solving the ground-state problem. The strategy presented here is
also applicable for many other quantum optimization and simulation tasks.
