  We present a general variational approach to determine the steady state of
open quantum lattice systems via a neural network approach. The steady-state
density matrix of the lattice system is constructed via a purified neural
network ansatz in an extended Hilbert space with ancillary degrees of freedom.
The variational minimization of cost functions associated to the master
equation can be performed using a Markov chain Monte Carlo sampling. As a first
application and proof-of-principle, we apply the method to the dissipative
quantum transverse Ising model.
