  Future quantum computation and networks require scalable monolithic circuits,
which incorporate various advanced functionalities on a single physical
substrate. Although substantial progress for various applications has already
been demonstrated on different platforms, the range of diversified manipulation
of photonic states on demand on a single chip has remained limited, especially
dynamic time management. Here, we demonstrate an electro-optic device,
including photon pair generation, propagation, electro-optical path routing, as
well as a voltage-controllable time delay of up to ~ 12 ps on a single Ti:LIbO3
waveguide chip. As an example, we demonstrate Hong-Ou-Mandel interference with
a visibility of more than 93$\pm$ 1.8\%. Our chip not only enables the
deliberate manipulation of photonic states by rotating the polarization but
also provides precise time control. Our experiment reveals that we have full
flexible control over single-qubit operations by harnessing the complete
potential of fast on-chip electro-optic modulation.
