A scalable classical verification reveals the gap of the state-of-the-art Gaussian Boson Sampling experiments*

Gaussian Boson Sampling (GBS) is one major candidate for establishing quantum computational advantage in the near term. Despite promising experimental progress, most existing validation schemes of GBS experiments merely rule out a few experimentally-motivated alternative physical hypotheses and fail to certify the device's output distribution directly, which is critical for establishing the computational hardness. Inspired by the symmetry property of Hafnian functions, we propose a scalable classical verification scheme of GBS, based on symmetry testing via a coarse-grained statistical heuristic, with strong theoretical and empirical evidence for its validity. Theoretically, when symmetry properties are approximately established, we prove that the device's output distribution is close to GBS under a mild assumption of the device. Empirically, based on classical simulation of up to 20 modes, we observe that our protocol can successfully distinguish GBS devices from all known alternative physical hypotheses and is further resilient to a small photon loss in the experiment. We perform part of our verification scheme on Xanadu's Borealis machine, which reveals a large inhomogeneity among alleged 216 squeezed modes that fail our symmetry test, and hence a gap for the claimed computational advantage based on GBS.