Validating quantum-supremacy experiments with exact and fast tensor network contraction
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The quantum circuits that declare quantum supremacy, such as Google Sycamore [Nature 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.
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