  Sources of quantum light, in particular correlated photon pairs that are
indistinguishable in all degrees of freedom, are the fundamental resource that
enables continuous-variable quantum computation and paradigms such as Gaussian
boson sampling. Nanophotonic systems offer a scalable platform for implementing
sources of indistinguishable correlated photon pairs. However, such sources
have so far relied on the use of a single component, such as a single waveguide
or a ring resonator, which offers limited ability to tune the spectral and
temporal correlations between photons. Here, we demonstrate the use of a
topological photonic system comprising a two-dimensional array of ring
resonators to generate indistinguishable photon pairs with dynamically tunable
spectral and temporal correlations. Specifically, we realize dual-pump
spontaneous four-wave mixing in this array of silicon ring resonators that
exhibits topological edge states. We show that the linear dispersion of the
edge states over a broad bandwidth allows us to tune the correlations, and
therefore, quantum interference between photons by simply tuning the two pump
frequencies in the edge band. Furthermore, we demonstrate energy-time
entanglement between generated photons. We also show that our topological
source is inherently protected against fabrication disorders. Our results pave
the way for scalable and tunable sources of squeezed light that are
indispensable for quantum information processing using continuous variables.
