Linear cross-entropy certification of quantum computational advantage in Gaussian Boson Sampling

TL;DR

This paper introduces a new validation method for Gaussian Boson Sampling experiments using a modified linear cross-entropy score, enabling direct comparison to ideal distributions and avoiding assumptions about computational hardness.

Contribution

It proposes the LXE score for validating GBS experiments against ideal models, bypassing the need to assume computational hardness of the ground truth distribution.

Findings

Analytical computation of the LXE score for lossless GBS.

Demonstration that LXE score can effectively validate GBS implementations.

Provides a framework to assess quantum advantage claims without relying on noise assumptions.

Abstract

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.