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arXiv:2009.07359 · Transactions on computational science and computational intelligence

What Have Google’s Random Quantum Circuit Simulation Experiments Demonstrated About Quantum Supremacy?

Jack K. Horner, John Symons

Published Jan 1, 2021• 5 citations
arXivHTMLPDF
DOI
10.1007/978-3-030-70873-3_29

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Recent experiments completed by collaborating research groups from Google, NASA Ames, UC Santa Barbara, and others provided compelling evidence that quantum supremacy has finally been achieved on a superconducting quantum processor. The theoretical basis for these experiments depends on sampling the output distributions of random quantum circuits; unfortunately, understanding how this theoretical basis can be used to define quantum supremacy is an extremely difficult task. Anyone attempting to understand how this sampling task relates to quantum supremacy must study concepts from random matrix theory, mathematical analysis, quantum chaos, computational complexity, and probability theory. Resources connecting these concepts in the context of quantum supremacy are scattered and often difficult to find. This article is an attempt to alleviate this difficulty in those who wish to understand the theoretical basis of Google's quantum supremacy experiments, by carefully walking through a derivation of their precise mathematical definition of quantum supremacy. It's designed for advanced undergraduate or graduate students who want more information than can be provided in popular science articles, but who might not know where to begin when tackling the many research papers related to quantum supremacy.
We propose a general tensor network method for simulating quantum circuits. The method is massively more efficient in computing a large number of correlated bitstring amplitudes and probabilities than existing methods. As an application, we study the sampling problem of Google's Sycamore circuits, which are believed to be beyond the reach of classical supercomputers and have been used to demonstrate quantum supremacy. Using our method, employing a small computational cluster containing 60 graphical processing units (GPUs), we have generated one million correlated bitstrings with some entries fixed, from the Sycamore circuit with 53 qubits and 20 cycles, with linear cross-entropy benchmark (XEB) fidelity equals 0.739, which is much higher than those in Google's quantum supremacy experiments.