  We show how to use the input-output formalism compute the propagator for an
open quantum system, i.e. quantum networks with a low dimensional quantum
system coupled to one or more loss channels. The total propagator is expressed
entirely in terms of the Green's functions of the low dimensional quantum
system, and it is shown that these Green's functions can be computed entirely
from the evolution of the low-dimensional system with an effective
non-hermitian Hamiltonian. Our formalism generalizes the previous works that
have focused on time independent Hamiltonians to systems with time dependent
Hamiltonians, making it a suitable computational tool for the analysis of a
number of experimentally interesting quantum systems. We illustrate our
formalism by applying it to analyze photon emission and scattering from driven
and undriven two-level system and three- level lambda system.
