  We present a Heisenberg operator based formulation of coherent quantum
feedback and Pyragas control. This model is easy to implement and allows for an
efficient and fast calculation of the dynamics of feedback-driven observables
as the number of contributing correlations grows in systems with a fixed number
of excitations only linearly in time. Furthermore, our model unravels the
quantum kinetics of entanglement growth in the system by explicitly calculating
non-Markovian multi-time correlations, e.g., how the emission of a photon is
correlated with an absorption process in the past. Therefore, the time-delayed
differential equations are expressed in terms of insightful physical
quantities. Another considerate advantage of this method is its compatibility
to typical approximation schemes, such as factorization techniques and the
semi-classical treatment of coherent fields. This allows the application on a
variety of setups, ranging from closed quantum systems in the few excitation
regimes to open systems and Pyragas control in general.
