  Verification of a quantum advantage in the presence of noise is a key open
problem in the study of near-term quantum devices. In this work, we show how to
assess the quality of photonic interference in a linear optical quantum device
(boson sampler) by using a maximum likelihood method to measure the strength at
which various noise sources are present in the experiment. This allows us to
use a sparse set of samples to test whether a given boson sampling experiment
meets known upper bounds on the level of noise permissible to demonstrate a
quantum advantage. Furthermore, this method allows us monitor the evolution of
noise in real time, creating a valuable diagnostic tool. Finally, we observe
that sources of noise in the experiment compound, meaning that the observed
value of the mutual photon indistinguishability, which is the main imperfection
in our study, is an effective value taking into account all sources of error in
the experiment.
