  We demonstrate non-equilibrium steady-state photon transport through a chain
of five coupled artificial atoms simulating the driven-dissipative Bose-Hubbard
model. Using transmission spectroscopy, we show that the system retains
many-particle coherence despite being coupled strongly to two open spaces. We
show that system energy bands may be visualized with high contrast using
cross-Kerr interaction. For vanishing disorder, we observe the transition of
the system from the linear to the nonlinear regime of photon blockade in
excellent agreement with the input-output theory. Finally, we show how
controllable disorder introduced to the system suppresses this non-local photon
transmission. We argue that proposed architecture may be applied to analog
simulation of many-body Floquet dynamics with even larger arrays of artificial
atoms paving an alternative way to demonstration of quantum supremacy
