  The detection of individual photons is an inherently binary mechanism,
revealing either their absence or presence while concealing their spectral
information. For multi-color imaging techniques, such as single photon
spectroscopy, fluorescence resonance energy transfer microscopy and
fluorescence correlation spectroscopy, wavelength discrimination is essential
and mandates spectral separation prior to detection. Here, we adopt an approach
borrowed from quantum photonic integration to realize a compact and scalable
waveguide-integrated single-photon spectrometer capable of parallel detection
on multiple wavelength channels, with temporal resolution below 50 ps and dark
count rates below 10 Hz. We demonstrate multi-detector devices for
telecommunication and visible wavelengths and showcase their performance by
imaging silicon vacancy color centers in diamond nanoclusters. The fully
integrated hybrid superconducting-nanophotonic circuits enable simultaneous
spectroscopy and lifetime mapping for correlative imaging and provide the
ingredients for quantum wavelength division multiplexing on a chip.
