Numerical solution of stochastic master equations using stochastic interacting wave functions
This work provides efficient numerical methods for simulating quantum measurement processes, addressing a computational bottleneck in quantum optics and open quantum systems.
The paper develops exponential numerical schemes for solving stochastic master equations with mixed initial states, representing the solution as a mixture of pure states. Simulations of two quantum measurement processes demonstrate the good performance of the new integrators.
We develop a new approach for solving stochastic quantum master equations with mixed initial states. 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 Schrödinger 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.