Verifying Quantum Advantage Experiments with Multiple Amplitude Tensor Network Contraction.

The quantum supremacy experiment, such as Google Sycamore [F. Arute et al., Nature (London) 574, 505 (2019).NATUAS0028-083610.1038/s41586-019-1666-5], poses a great challenge for classical verification due to the exponentially increasing compute cost. Using a new-generation Sunway supercomputer within 8.5 d, we provide a direct verification by computing 3×10^{6} exact amplitudes for the experimentally generated bitstrings, obtaining a cross-entropy benchmarking fidelity of 0.191% (the estimated value is 0.224%). The leap of simulation capability is built on a multiple-amplitude tensor network contraction algorithm which systematically exploits the "classical advantage" (the inherent "store-and-compute" operation mode of von Neumann machines) of current supercomputers, and a fused tensor network contraction algorithm which drastically increases the compute efficiency on heterogeneous architectures. Our method has a far-reaching impact in solving quantum many-body problems, statistical problems, as well as combinatorial optimization problems.

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 ∼600 yr using exact methods, whereas our quantum computer, Jiǔzhang 3.0, takes only 1.27 µs to produce a sample. Generating the hardest sample from the experiment using an exact algorithm would take Frontier∼3.1×10^{10} yr.