  Analyzing the properties of complex quantum systems is crucial for further
development of quantum devices, yet this task is typically challenging and
demanding with respect to required amount of measurements. A special attention
to this problem appears within the context of characterizing outcomes of noisy
intermediate-scale quantum devices, which produce quantum states with specific
properties so that it is expected to be hard to simulate such states using
classical resources. In this work, we address the problem of characterization
of a boson sampling device, which uses interference of input photons to produce
samples of non-trivial probability distributions that at certain condition are
hard to obtain classically. For realistic experimental conditions the problem
is to probe multi-photon interference with a limited number of the measurement
outcomes without collisions and repetitions. By constructing networks on the
measurements outcomes, we demonstrate a possibility to discriminate between
regimes of indistinguishable and distinguishable bosons by quantifying the
structures of the corresponding networks. Based on this we propose a
machine-learning-based protocol to benchmark a boson sampler with unknown
scattering matrix. Notably, the protocol works in the most challenging regimes
of having a very limited number of bitstrings without collisions and
repetitions. As we expect, our framework can be directly applied for
characterizing boson sampling devices that are currently available in
experiments.
