  An efficient algorithm to simulate dynamics of open quantum system is
presented. The method describes the dynamics by unraveling stochastic wave
functions converging to a density operator description. The stochastic
techniques are based on the quantum collision model. Modeling systems dynamics
by wave functions and modeling the interaction with the environment with a
collision sequence reduces the complexity scale significantly. The algorithm
developed, can be implemented on quantum computers. We introduce stochastic
methods that exploit statistical characters of the model, as Markovianity,
Brownian motion and binary distribution. The central limit theorem is employed
to study the convergence of distributions of stochastic dynamics of pure
quantum states represented by wave vectors. By averaging a sample of functions
in the distribution we prove and demonstrate the convergence of the dynamics to
the mixed quantum state described by a density operator.
