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Computer

Beyond Quantum Supremacy

Erik P. DeBenedictis

Published Feb 1, 2020• 4 citations
Publisher

Abstract

Demonstrations of quantum supremacy have become convincing enough that it's time to think seriously about what comes next.
DOI
10.1109/mc.2019.2958446

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Results on the hardness of approximate sampling are seen as important stepping stones toward a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include boson sampling, instantaneous quantum polynomial time (IQP) circuit sampling, and universal random circuit sampling. A key challenge for any such demonstration is to certify the correct implementation. For all these examples, and in fact for all sufficiently flat distributions, we show that any noninteractive certification from classical samples and a description of the target distribution requires exponentially many uses of the device. Our proofs rely on the same property that is a central ingredient for the approximate hardness results, namely, that the sampling distributions, as random variables depending on the random unitaries defining the problem instances, have small second moments.