Constructing neural stationary states for open quantum many-body systems

Abstract

We propose a new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems. Using the high expressive power of the variational ansatz described by the restricted Boltzmann machines, which we dub as the neural stationary state ansatz, we compute the stationary states of quantum dynamics obeying the Lindblad 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.

9 pages, 7 figures

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• Variational neural network ansatz for steady states in open quantum systems
• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
• On the complexity of the steady-state of weakly symmetric open quantum lattices
• A Tensor Network Approach to Finite Markov Decision Processes
• The deep learning and statistical physics applications to the problems of combinatorial optimization