  We propose to use the complex quantum dynamics of a massive particle in a
non-quadratic potential to reconstruct an initial unknown motional quantum
state. We theoretically show that the reconstruction can be efficiently done by
measuring the mean value and the variance of the position quantum operator at
different instances of time in a quartic potential. We train a neural network
to successfully solve this hard regression problem. We discuss the experimental
feasibility of the method by analyzing the impact of decoherence and
uncertainties in the potential.
