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).], 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 $3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ 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.