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We report new Gaussian boson sampling experiments withpseudo-photon-number-resolving detection, which register up to 255 photon-clickevents. We consider partial photon distinguishability and develop a morecomplete model for the characterization of the noisy Gaussian boson sampling.In the quantum computational advantage regime, we use Bayesian tests andcorrelation function analysis to validate the samples against all currentclassical mockups. Estimating with the best classical algorithms to date,generating a single ideal sample from the same distribution on thesupercomputer Frontier would take ~ 600 years using exact methods, whereas ourquantum computer, Jiuzhang 3.0, takes only 1.27 us to produce a sample.Generating the hardest sample from the experiment using an exact algorithmwould take Frontier ~ 3.1*10^10 years.

Gaussian Boson Sampling with Pseudo-Photon-Number Resolving Detectors and Quantum Computational Advantage