The quantum circuits that declare quantum supremacy, such as Google Sycamore
[Nature \textbf{574}, 505 (2019)], raises a paradox in building reliable result
references. While simulation on traditional computers seems the sole way to
provide reliable verification, the required run time is doomed with an
exponentially-increasing compute complexity. To find a way to validate current
``quantum-supremacy" circuits with more than 50 qubits, we propose a
simulation method that exploits the ``classical advantage" (the inherent
``store-and-compute" operation mode of von Neumann machines) of current
supercomputers, and computes uncorrelated amplitudes of a random quantum
circuit with an optimal reuse of the intermediate results and a minimal memory
overhead throughout the process. Such a reuse strategy reduces the original
linear scaling of the total compute cost against the number of amplitudes to a
sublinear pattern, with greater reduction for more amplitudes. Based on a
well-optimized implementation of this method on a new-generation Sunway
supercomputer, we directly verify Sycamore by computing three million exact
amplitudes for the experimentally generated bitstrings, obtaining an XEB
fidelity of 0.191% which closely matches the estimated value of 0.224%.
Our computation scales up to 41,932,800 cores with a sustained
single-precision performance of 84.8 Pflops, which is accomplished within
8.5 days. Our method has a far-reaching impact in solving quantum many-body
problems, statistical problems as well as combinatorial optimization problems
where one often needs to contract many tensor networks which share a
significant portion of tensors in common.Comment: 7 pages, 4 figures, comments are welcome