  As superconductor quantum technologies are moving towards large-scale
integrated circuits, a robust and flexible approach to routing photons at the
quantum level becomes a critical problem. Active circuits, which contain
parametrically driven elements selectively embedded in the circuit offer a
viable solution. Here, we present a general strategy for routing
nonreciprocally quantum signals between two sites of a given lattice of
oscillators, implementable with existing superconducting circuit components.
Our approach makes use of a dual lattice of overdamped oscillators linking the
nodes of the main lattice. Solutions for spatially selective driving of the
lattice elements can be found, which optimally balance coherent and dissipative
hopping of microwave photons to nonreciprocally route signals between two given
nodes. In certain lattices these optimal solutions are obtained at the
exceptional point of the dynamical matrix of the network. We also demonstrate
that signal and noise transmission characteristics can be separately optimized.
