Simulating Gaussian boson sampling experiments with phase-space representations*

In the past few years, an increasing number of large-scale Gaussian boson sampling (GBS) quantum computers have claimed quantum advantage. These devices are linear photonic networks whose inputs are squeezed vacuum states and outputs are photon coincidence counts, where the probability of measuring a specific count pattern is #P -hard to compute.

The current generation of GBS has recorded up to 219 -th and 255 -th order coincidence counts on programmable and static networks, respectively, well beyond the realm of direct classical computation. This leads to an interesting problem: How does one verify experimental outputs when the high-order quantum correlations are intractably hard to calculate?

To answer this, we use grouped probabilities simulated using the positive-P phase-space representation. These have the same moments as experimental outputs, but are computable. Such methods allow one to simulate all correlations generated in the network, within sampling error. We present comparisons of theory versus experiment for data from recent experiments, quantifying differences using χ² tests. Our results show increased agreement with experimental outputs once additional decoherence is added and the transmission efficiency is corrected.