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

We report new Gaussian boson sampling experiments with pseudo-photon-number-resolving detection, which register up to 255 photon-click events. We consider partial photon distinguishability and develop a more complete model for the characterization of the noisy Gaussian boson sampling. In the quantum computational advantage regime, we use Bayesian tests and correlation function analysis to validate the samples against all current classical spoofing mockups. Estimating with the best classical algorithms to date, generating a single ideal sample from the same distribution on the supercomputer Frontier would take $\ensuremath{\sim}600\text{ }\text{ }\mathrm{yr}$ using exact methods, whereas our quantum computer, Ji\ifmmode \check{u}\else \v{u}\fi{}zh\ifmmode \bar{a}\else \={a}\fi{}ng 3.0, takes only $1.27\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{s}$ to produce a sample. Generating the hardest sample from the experiment using an exact algorithm would take $\mathrm{Frontier}\ensuremath{\sim}3.1\ifmmode\times\else\texttimes\fi{}{10}^{10}\text{ }\text{ }\mathrm{yr}$.