Classical Simulability of Gaussian Boson Sampling

We investigate the presence of quantum advantage in boson sampling experiments by crafting classical simulations that can efficiently replicate the empirical outcomes of some recent experiments. Our approach builds upon established classical models of multi-photon entangled states and non-Gaussian measurements while introducing two pivotal innovations: the representation of Gaussian multi-photon states as correlated Gaussian random vectors and the integration of non-Gaussian measurements via a deterministic model of amplitude threshold crossing events. These modeling concepts have displayed the capability to replicate quantum phenomena, providing a potent toolkit to identify quantum advantage and demarcate the quantum/classical boundary in photonic systems. Our classical simulation agrees well with experimentally produced outcomes in terms of average counts and k-order correlations, demonstrating the efficient classical simulabilty of these boson sampling experiments.