Wave function realization of a thermal collision model

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.