Validating quantum-supremacy experiments with exact and fast tensor network contraction

The quantum supremacy experiment, such as Google Sycamore [Nature 574, 505 (2019)], poses great challenge for classical verification due to the exponentially-increasing compute cost. Using a new-generation Sunway supercomputer within 8.5 days, we provide a direct verification by computing three million exact amplitudes for the experimentally generated bitstrings, obtaining an XEB 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.