Linear cross-entropy certification of quantum computational advantage in Gaussian Boson Sampling
arxiv(2024)
摘要
Validation of quantum advantage claims in the context of Gaussian Boson
Sampling (GBS) currently relies on providing evidence that the experimental
samples genuinely follow their corresponding ground truth, i.e., the
theoretical model of the experiment that includes all the possible losses that
the experimenters can account for. This approach to verification has an
important drawback: it is necessary to assume that the ground truth
distributions are computationally hard to sample, that is, that they are
sufficiently close to the distribution of the ideal, lossless experiment, for
which there is evidence that sampling, either exactly or approximately, is a
computationally hard task. This assumption, which cannot be easily confirmed,
opens the door to classical algorithms that exploit the noise in the ground
truth to efficiently simulate the experiments, thus undermining any quantum
advantage claim. In this work, we argue that one can avoid this issue by
validating GBS implementations using their corresponding ideal distributions
directly. We explain how to use a modified version of the linear cross-entropy,
a measure that we call the LXE score, to find reference values that help us
assess how close a given GBS implementation is to its corresponding ideal
model. Finally, we analytically compute the score that would be obtained by a
lossless GBS implementation.
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