  We present a class of exponential integrators to compute solutions of the
stochastic Schr\"odinger equation arising from the modeling of open quantum
systems. In order to be able to implement the methods within the same framework
as the deterministic counterpart, we express the solution using the Kunita's
representation. With appropriate truncations, the solution operator can be
written as matrix exponentials, which can be efficiently implemented by the
Krylov subspace projection. The accuracy is examined in terms of the strong
convergence, by comparing trajectories, and the weak convergence, by comparing
the density-matrix operator. We show that the local accuracy can be further
improved by introducing a third-order commutator in the exponential. The
effectiveness of the proposed methods is tested using the example from Di
Ventra et al. [Journal of Physics: Condensed Matter, 2004].
