  Topological quantum optics, an emerging area of study, holds the potential to
bring about substantial enhancements for integrated quantum devices. Here we
propose integrated topological quantum devices performing various functions
including optical parametric amplification, frequency division, and frequency
entangled biphoton generation. We show two distinct edge modes corresponding to
different frequency ranges in both sandwich kagome and honeycomb topological
designs that emulate the quantum valley Hall effect. These two topological edge
modes enable two types of optical parametric processes through four-wave
mixing, specifically inter-band and intra-band cases. The devices emulating
photonic valley-Hall insulators allow the frequency division of two transverse
modes, and furthermore, enable the separation of two quantum functionalities -
optical parametric amplification and frequency entangled biphoton state
generation. More importantly, the parametric processes are inborn topological
protected, showing robustness against sharp bends and disorders. Our proposal
significantly widens the possibilities for robust, multifunctional topological
quantum devices on-chip, which may find applications in quantum information
processing.
