Gaussian-boson-sampling-enhanced dense subgraph finding shows limited advantage over efficient classical algorithms

Abstract: Recent claims of achieving exponential quantum advantage have attracted attention to Gaussian boson sampling (GBS), a potential application of which is dense subgraph finding. We investigate the effects of sources of error including loss and spectral impurity on GBS applied to dense subgraph finding algorithms. We find that the effectiveness of these algorithms is remarkably robust to errors, to such an extent that there exist efficient classical algorithms that can simulate the underlying GBS. These results imply that the speedup of GBS-based algorithms for the dense subgraph problem over classical approaches is at most polynomial, though this could be achieved on a quantum device with dramatically less stringent requirements on loss and photon purity than general GBS.