  Synchronization is a major concept in nonlinear physics. In a large number of
systems, it is observed at long times for a sinusoidal excitation. In this
paper, we design a transiently non-sinusoidal driving to reach the
synchronization regime more quickly. We exemplify an inverse engineering method
to solve this issue on the classical Van der Pol oscillator. This approach
cannot be directly transposed to the quantum case as the system is no longer
point-like in phase space. We explain how to adapt our method by an iterative
procedure to account for the finite-size quantum distribution in phase space.
We show that the resulting driving yields a density matrix close to the
synchronized one according to the trace distance. Our method provides an
example of fast control of a nonlinear quantum system, and raises the question
of the quantum speed limit concept in the presence of nonlinearities.
