Quantum transport in open spin chains using neural-network quantum states

In this work we study the treatment of asymmetric open quantum systems with neural networks based on the restricted Boltzmann machine. In particular, we are interested in the nonequilibrium steady-state current in the boundary-driven (anisotropic) Heisenberg spin chain. We address previously published difficulties in treating asymmetric dissipative systems with neural-network quantum states and Monte Carlo sampling and present an optimization method and a sampling technique that can be used to obtain high-fidelity steady-state approximations of such systems. We point out some inherent symmetries of the Lindblad operator under consideration and exploit them during sampling. We show that local observables are not always a good indicator of the quality of the approximation and finally present results for the spin current that are in agreement with known results of simple open Heisenberg chains.