Rolando Biscay, Joaquin Fernández, Carlos M. Mora:
Numerical solution of stochastic master equations using stochastic interacting wave functions
We develop a new approach for solving stochastic quantum master equations with mixed initial states. We focus on finite dimensional quantum state spaces. First, we obtain that the solution of the jump-diffusion stochastic master equation is represented by a mixture of pure states satisfying a system of stochastic differential equations of Schrödinger type. Then, we design three exponential schemes for these coupled stochastic Schr¨dinger equations, which are driven by Brownian motions and jump processes. Hence, we have constructed efficient numerical methods for the stochastic master equations based on quantum trajectories. The good performance of the new numerical integrators is illustrated by simulations of two quantum measurement processes.