  We propose a simple quantum algorithm for simulating highly oscillatory
quantum dynamics, which does not require complicated quantum control logic for
handling time-ordering operators. To our knowledge, this is the first quantum
algorithm that is both insensitive to the rapid changes of the time-dependent
Hamiltonian and exhibits commutator scaling. Our method can be used for
efficient Hamiltonian simulation in the interaction picture. In particular, we
demonstrate that for the simulation of the Schr\"odinger equation, our method
exhibits superconvergence and achieves a surprising second order convergence
rate, of which the proof rests on a careful application of pseudo-differential
calculus. Numerical results verify the effectiveness and the superconvergence
property of our method.
