Time evolution of quasi probability distributions using the variational Monte Carlo approach

Time evolved quasi-probability distributions in the phase space offer an alternative to solving the Lindblad master equation for open systems in large Hilbert spaces. However, these partial differential equations are prohibitively difficult to integrate numerically in more than a 2d phase space using conventional methods such as finite elements. Facing similar difficulties, variational Monte Carlo approaches combined with machine learning approximations of the quantum wave function have proven successful in both ground state estimations for complex systems and their time evolution [1]. We now employ this variational principle for the time evolution of quasi-probability distributions. We show feasibility examples for the truncated Wigner and Husimi Q functions.

1. Carleo, G., & Troyer, M. (2017). Solving the quantum many-body problem with artificial neural networks. Science, 355(6325), 602–606.