Gaussian boson sampling: Determining quantum advantage

A Gaussian Boson Sampler (GBS) is a non-universal optical quantum computer designed to unequivocally demonstrate quantum advantage. The output distributions of such devices are #P-hard to compute or sample from, leading to multiple large-scale experiments claiming quantum advantage.

This has prompted the design of classical algorithms that sample an approximate output distribution. It is claimed that such algorithms produce samples that are closer to the ideal GBS distribution than the experiment, and hence that this constitutes a refutation of quantum advantage. But how does one verify which claims are accurate? Importantly, given that there are sources of experimental errors and decoherence, can one claim any quantum advantage for a modified task, of generating the non-ideal output samples?

To this end, we compare experiments and classical samplers, including a new phase-space sampler that scales with the classicality of the outputs, with a best fit quantum model for the experimental data, using chi-squared tests. For the GBS model, we use positive-P phase-space simulators that efficiently generate binned moments and correlations of any order. This allows one to determine whether quantum advantage has been achieved for the task of generating non-ideal GBS.