  Quantum input-output response analysis is a useful method for modeling the
dynamics of complex quantum networks, such as those for communication or
quantum control via cascade connections. Non-Markovian effects have not yet
been studied in such networks. Here we extend the Markovian input-output
network formalism developed in optical systems to non-Markovian cascaded
networks which can be used, e.g., to analyze the input-output response of
mesoscopic quantum networks. We use this formalism to explore the behavior of
superconducting qubit networks, where we examine the effect of finite cavity
bandwidths. We also discuss its application to open- and closed-loop control
networks, and show how these networks create effective Hamiltonians for the
controlled system.
