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arXiv · 1812.01023

Sample complexity of device-independently certified "quantum supremacy"

Dominik Hangleiter·Martin Kliesch·Jens Eisert·Christian Gogolin
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Abstract

Results on the hardness of approximate sampling are seen as important stepping stones towards a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include boson sampling, 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 non-interactive 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.

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Dominik Hangleiter, Martin Kliesch, Jens Eisert, Christian Gogolin. 2018-12-03. Sample complexity of device-independently certified "quantum supremacy". https://doi.org/10.1103/physrevlett.122.210502

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