  Topological photonics has been introduced as a powerful platform for
integrated optics, since it can deal with robust light transport, and be
further extended to the quantum world. Strikingly, valley-contrasting physics
in topological photonic structures contributes to valley-related edge states,
their unidirectional coupling, and even valley-dependent wave-division in
topological junctions. Here, we design and fabricate nanophotonic topological
harpoon-shaped beam splitters (HSBSs) based on $120$-deg-bending interfaces and
demonstrate the first on-chip valley-dependent quantum information process.
Two-photon quantum interference, namely, HongOu-Mandel (HOM) interference with
a high visibility of $0.956 \pm 0.006$, is realized with our 50/50 HSBS, which
is constructed by two topologically distinct domain walls. Cascading this kind
of HSBS together, we also demonstrate a simple quantum photonic circuit and
generation of a path-entangled state. Our work shows that the photonic valley
state can be used in quantum information processing, and it is possible to
realize more complex quantum circuits with valley-dependent photonic
topological insulators, which provides a novel method for on-chip quantum
information processing.
