Bayesian approach to Boson sampling validation

The Boson sampling problem consists in sampling from the output probability distribution of a bosonic Fock state, after it evolves through a linear interferometer. There is strong evidence that Boson sampling is computationally hard for classical computers, while it can be solved naturally by bosons. This has led it to draw increasing attention as a possible way to provide experimental evidence for the quantum computational supremacy. Nevertheless, the very complexity of the problem makes it hard to exclude the hypothesis that the experimental data are sampled from a different probability distribution. By exploiting integrated quantum photonics, we have carried out a set of three-photon Boson sampling experiments and analyzed the results using a Bayesian approach, showing that it represents a valid alternative to currently used methods. We adopt this approach to provide evidence that the experimental data correspond to genuine three-photon interference, validating the results against fully and partially-distinguishable photon hypotheses.