Online Seminar: Xun Gao (Harvard University), “Understanding the Linear Cross Entropy Benchmark through a Statistical Physics Model”
Date and Time
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Location: Zoom https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09
Time: Tuesday, May 11, 2021, 10:00 AM (Eastern US), 15:00 (UK/Eire), 16:00 (Central Europe), 22:00 (China)
Title: Understanding the Linear Cross Entropy Benchmark through a Statistical Physics Model
Abstract: In a recent experiment, Google claimed to achieve quantum advantage based on sampling from random quantum circuits. To certify the correctness of the sampling task, they developed a linear cross- entropy benchmark (XEB) and made their claim based on achieving a high value of XEB. The implicit assumption made in Google’s claim is that XEB approximates the fidelity well and hence could serve as a proxy in practice. However, it turns out that XEB can often deviate from fidelity, so it is crucial to understand how XEB and fidelity are related. I introduce a novel approach to analyze XEB through a mapping of random quantum circuits to a discrete classical statistical-physics diffusion-reaction model. By analyzing this model both qualitatively and numerically, we show that XEB usually overestimates fidelity These results indicate that one needs a new benchmark to certify quantum advantage.
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