Numerical solution of stochastic master equations using stochastic interacting wave functions

TL;DR

This paper introduces a novel numerical approach for solving stochastic quantum master equations by representing solutions as mixtures of pure states and developing efficient exponential schemes for the associated stochastic Schrödinger equations, demonstrated through quantum measurement simulations.

Contribution

The paper presents a new method that transforms stochastic master equations into coupled stochastic Schrödinger equations and designs exponential schemes for their numerical integration.

Findings

Efficient numerical schemes outperform existing methods.

Simulations accurately model quantum measurement processes.

Mixture of pure states simplifies the solution of stochastic master equations.

Abstract

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 Schr\"odinger type. Then, we design three exponential schemes for these coupled stochastic Schr\"odinger 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.