Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation

The theory of open quantum systems is crucial for quantum science and engineering. Simulations of such systems are computationally expensive due to the exponential growth of the extended Hilbert spaces' dimensionality. We propose an efficient machine learning approach to simulate such dynamics using a probabilistic formulation of quantum mechanics based on the positive operator-valued measure, parameterizing the quantum states with autoregressive neural networks for exact sampling. In addition, we use the String States to improve local correlations and partially restore symmetries. We solve for the dynamics using the forward-backward trapezoid method and for the steady-state solution variationally. We benchmark our algorithms on one- and two-dimensional systems. The results are significantly more accurate than other approaches using restricted Boltzmann machines with Markov chain Monte Carlo sampling. This work shows an efficient approach to solve quantum dynamics as well as high-dimensional probabilistic differential equations, which provides a general method to understand both quantum and classical phenomena in various contexts.

arxiv:2009.05580