Efficient propagation of stochastic open quantum dynamics in coordinate space

Accurate and fast numerical solutions of the master equation in Lindblad form are important to manipulate a great variety of quantum systems for the development of quantum technologies. However, modeling strongly interacting quantized degrees of freedom is a fundamental problem due to an exponential scaling of Hilbert space. We solve the Lindblad quantum master equation by propagating quantum state trajectories in coordinate space, which involves stochastic quantum jumps. The propagation in coordinate space is performed using the multi-configuration time dependent Hartree (MCTDH) method that considerably reduces the Hilbert space or the number of equations of motion for strongly coupled oscillators. For scenarios with the number of excitations higher than one, we show the potential of our methodology in comparison with exact solutions of the density matrix in physical systems of interest in cavity quantum electrodynamics [1]. We demonstrate that it is possible to perform efficient propagations in low-RAM machines in systems whose solution with traditional methodologies requires high-RAM machines. This methodology is independent of the system under study and also works with time dependent Hamiltonians.

[1] J.F. Triana, F. Herrera, arXiv:2208.01217