Reduced operator approximation for modelling open quantum systems

We present the Reduced Operator Approximation: a simple, physically transparent and computationally efficient method of modelling open quantum systems. It employs the Heisenberg picture of the quantum dynamics, which allows us to focus on the system degrees of freedom in a natural and easy way. We describe different variants of the method, low- and high-order (including the interaction operators), defining them for either general quantum harmonic oscillators baths or specialising them for independent baths with Lorentzian spectral densities. They are applied to different systems (coupled to different baths with different strengths) and compared with the exact pseudomode and the popular quantum state diffusion method