  Multi-photon interference is at the heart of photonic quantum technologies.
Arrays of integrated cavities can support bright sources of single-photons with
high purity and small footprint, but the inevitable spectral distinguishability
between photons generated from non-identical cavities is an obstacle to
scaling. In principle, this problem can be alleviated by measuring photons with
high timing resolution, which erases spectral information through the
time-energy uncertainty relation. Here, we experimentally demonstrate that
detection can be implemented with a temporal resolution sufficient to interfere
photons detuned on the scales necessary for cavity-based integrated photon
sources. By increasing the effective timing resolution of the system from 200ps
to 20ps, we observe a 20% increase in the visibility of quantum interference
between independent photons from integrated micro-ring resonator sources that
are detuned by 6.8GHz. We go on to show how time-resolved detection of
non-ideal photons can be used to improve the fidelity of an entangling
operation and to mitigate the reduction of computational complexity in boson
sampling experiments. These results pave the way for photonic quantum
information processing with many photon sources without the need for active
alignment.
