Process characterization with Monte Carlo wave functions

We present an efficient method to simulate a quantum process subject to dissipation and noise. To describe the effect on any input state we evolve Monte Carlo wave functions for a principal and ancilla system, prepared initially in an entangled state. In analogy to experimental process tomography, the simulated propagator for the system density matrix is conveniently described by a process chi matrix - directly determined from the stochastic state vectors. Our method significantly reduces the computational complexity compared with standard theoretical characterization methods. It also delivers an upper bound on the trace distance between the ideal and simulated process based on the evolution of only a single wave function of the entangled system.