  We study the optimal control formulation for stochastic nonlinear Schrodinger
equation (SNLSE) on a finite graph.
  By viewing the SNLSE as a stochastic Wasserstein Hamiltonian flow on density
manifold, we show the global existence of a unique strong solution for SNLSE
with a linear drift control or a linear diffusion control on graph.
Furthermore, we provide the gradient formula, the existence of the optimal
control and a description on the optimal condition via the forward and backward
stochastic differential equations.
