Effect of photonic errors on quantum enhanced dense-subgraph finding

We investigate the effects of photon loss and spectrally impure sources on Gaussian boson sampling (GBS) when used in dense-subgraph-finding algorithms. We find that the effectiveness of these algorithms is remarkably robust to such errors, to such an extent that there exist classical algorithms that can efficiently simulate the underlying GBS. These results suggest that, unlike the GBS problem itself, the speed-up of GBS-based algorithms over classical approaches when applied to the dense-subgraph problem is not exponential. They do suggest, however, that any advantage offered could be achieved on a quantum device with far less stringent requirements on photon loss and purity than general GBS.