  In this paper, we show that quantum feedback control may be applied to
generate desired states for atomic and photonic systems based on a
semi-infinite waveguide coupled with multiple two-level atoms. In this set-up,
an initially excited atom can emit one photon into the waveguide, which can be
reflected by the terminal mirror or other atoms to establish different feedback
loops via the coherent interactions between the atom and photon. When there are
at most two excitations in the waveguide quantum electrodynamics (waveguide
QED) system, the evolution of quantum states can be interpreted using random
graph theory. While this process is influenced by the environment, and we
clarify that the environment-induced dynamics can be eliminated by
measurement-based feedback control or coherent drives. Thus, in the open system
atom-waveguide interactions, measurement-based feedback can modulate the final
steady quantum state, while simultaneously, the homodyne detection noise in the
measurement process can induce oscillations, which is treated by the coherent
feedback designs.
