  While integrated photonics is a robust platform for quantum information
processing, architectures for photonic quantum computing place stringent
demands on high quality information carriers. Sources of single photons that
are highly indistinguishable and pure, that are either near-deterministic or
heralded with high efficiency, and that are suitable for mass-manufacture, have
been elusive. Here, we demonstrate on-chip photon sources that simultaneously
meet each of these requirements. Our photon sources are fabricated in silicon
using mature processes, and exploit a novel dual-mode pump-delayed excitation
scheme to engineer the emission of spectrally pure photon pairs through
intermodal spontaneous four-wave mixing in low-loss spiralled multi-mode
waveguides. We simultaneously measure a spectral purity of $0.9904 \pm 0.0006$,
a mutual indistinguishably of $0.987 \pm 0.002$, and $>90\%$ intrinsic
heralding efficiency. We measure on-chip quantum interference with a visibility
of $0.96 \pm 0.02$ between heralded photons from different sources. These
results represent a decisive step for scaling quantum information processing in
integrated photonics.
