  Levitated nanoparticles provide a controllable and isolated platform for
probing fundamental quantum phenomena at the macroscopic scale. In this work,
we introduce an optimization method to determine optimal static potentials for
the generation of largely delocalized and non-Gaussian quantum states of
levitated nanoparticles. Our optimization strategy accounts for
position-dependent noise sources originating from the fluctuations of the
potential. We provide key figures of merit that allow for fast computation and
capture relevant features of the dynamics, mitigating the computational demands
associated with the multiscale simulation of this system. Specifically, we
introduce coherence length and coherent cubicity as signatures of large
delocalization and quantum non-Gaussian states, respectively. We apply the
optimization approach to a family of quartic potentials and show that the
optimal configuration depends on the strength and nature of the noise in the
system. Additionally, we benchmark our results with the full quantum dynamics
simulations of the system for the optimal potentials.
