  Boson Sampling is a computational task strongly believed to be hard for
classical computers, but efficiently solvable by orchestrated bosonic
interference in a specialised quantum computer. Current experimental schemes,
however, are still insufficient for a convincing demonstration of the advantage
of quantum over classical computation. A new variation of this task,
Scattershot Boson Sampling, leads to an exponential increase in speed of the
quantum device, using a larger number of photon sources based on parametric
downconversion. This is achieved by having multiple heralded single photons
being sent, shot by shot, into different random input ports of the
interferometer. Here we report the first Scattershot Boson Sampling
experiments, where six different photon-pair sources are coupled to integrated
photonic circuits. We employ recently proposed statistical tools to analyse our
experimental data, providing strong evidence that our photonic quantum
simulator works as expected. This approach represents an important leap toward
a convincing experimental demonstration of the quantum computational supremacy.
