  We develop a real-time Full Configuration Interaction Quantum Monte Carlo
approach for the modeling of driven-dissipative open quantum systems. The
method enables stochastic sampling of the Liouville-von-Neumann time evolution
of the density matrix, thanks to a massively parallel algorithm, thus providing
estimates of observables on the non-equilibrium steady state. We present the
underlying theory, and introduce initiator technique and importance sampling to
reduce the statistical error. Finally, we demonstrate the efficiency of our
approach by applying it to the driven- dissipative two-dimensional XYZ spin
model on lattice.
