  In this paper, we consider the numerical solution of a nonlinear Schrodinger
equation with spatial random potential. The randomly shifted quasi-Monte Carlo
(QMC) lattice rule combined with the time-splitting pseudospectral
discretization is applied and analyzed. The nonlinearity in the equation
induces difficulties in estimating the regularity of the solution in random
space. By the technique of weighted Sobolev space, we identify the possible
weights and show the existence of QMC that converges optimally at the
almost-linear rate without dependence on dimensions. The full error estimate of
the scheme is established. We present numerical results to verify the accuracy
and investigate the wave propagation.
