Validation of a noisy Gaussian boson sampler via graph theory

Quantum photonic processors are emerging as promising platforms to prove preliminary evidence of quantum computational advantage toward the realization of universal quantum computers. In the context of nonuniversal noisy intermediate quantum devices, photonic-based sampling machines solving the Gaussian boson sampling (GBS) problem currently play a central role in the experimental demonstration of quantum computational advantage. A relevant issue is the validation of the sampling process in the presence of experimental noise, such as photon losses, which could undermine the hardness of simulating the experiment. We test the capability of a validation protocol that exploits the connection between GBS and graph perfect match counting to perform such an assessment in a noisy scenario. In particular, we use as a test bench the recently developed machine Borealis, a large-scale sampling machine that has been made available online for external users, and address its operation in the presence of noise. The employed approach to validation is also shown to provide connections with the open question on the effective advantage of using noisy GBS devices for graph similarity and isomorphism problems and thus provides an effective method for certification of quantum hardware.