Designing neural networks for stationary states in open quantum many-body systems

We propose a new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems [1]. Using the high expressive power of the variational ansatz described by the restricted Boltzmann machines [2], which we dub as the neural stationary state ansatz, we compute the stationary states of quantum dynamics obeying the homogeneous Markovian quantum master equations. The mapping of the stationary-state search problem into finding a zero-energy ground state of an appropriate Hermitian operator allows us to apply the conventional variational Monte Carlo method for the optimization. Our method is shown to simulate various spin systems efficiently, i.e., the transverse-field Ising models in both one and two dimensions and the XYZ model in one dimension.

[1] N. Yoshioka and R. Hamazaki, Phys. Rev. B 99, 214306 (2019).
[2] G. Carleo and M. Troyer, Science 355, 602 (2017).