  Numerical stochastic integration is a powerful tool for the investigation of
quantum dynamics in interacting many body systems. As with all numerical
integration of differential equations, the initial conditions of the system
being investigated must be specified. With application to quantum optics in
mind, we show how various commonly considered quantum states can be numerically
simulated by the use of widely available Gaussian and uniform random number
generators. We note that the same methods can also be applied to computational
studies of Bose-Einstein condensates, and give some examples of how this can be
done.
