  Feedback amplification is a key technique for synthesizing various important
functionalities, especially in electronic circuits involving op-amps. This
paper presents a quantum version of this methodology, where the general
phase-preserving quantum amplifier and coherent (i.e., measurement-free)
feedback are employed to construct various type of systems having useful
functionalities: quantum versions of differentiator, integrator,
self-oscillator, and active filters. The class of active filters includes the
Butterworth filter, which can be used to enhance the capacity of an optical
quantum communication channel, and the non-reciprocal amplifier, which enables
measurement of a superconducting qubits system as well as protection of it by
separating input from output fields. A particularly detailed investigation is
performed on the active phase-cancelling filter for realizing a broadband
gravitational-wave detector; that is, the feedback amplification method is used
to construct an active filter that compensates the phase delay of the signal
and eventually recovers the sensitivity in the high frequency regime.
