  In this paper, we study the semiclassical Schr\"odinger equation with random
parameters and develop several robust multi-fidelity methods. We employ the
time-splitting Fourier pseudospectral (TSFP) method for the high-fidelity
solver, and consider different low-fidelity solvers including the meshless
method like frozen Gaussian approximation (FGA) and the level set (LS) method
for the semiclassical limit of the Schr\"odinger equation. With a careful
choice of the low-fidelity model, we obtain an error estimate for the
bi-fidelity method. We conduct numerous numerical experiments and validate the
accuracy and efficiency of our proposed multi-fidelity methods, by comparing
the performance of a class of bi-fidelity and tri-fidelity approximations.
