Gaussian boson sampling at finite temperature

Gaussian boson sampling (GBS) is a promising candidate for an experimental demonstration of quantum advantage using photons. However, sufficiently large noise might hinder a GBS implementation from entering the regime where quantum speedup is achievable. Here, we investigate how thermal noise affects the classical intractability of generic quantum optical sampling experiments, GBS being a particular instance of the latter. We do so by establishing sufficient conditions for an efficient simulation to be feasible, expressed in the form of inequalities between the relevant parameters that characterize the system and its imperfections. We demonstrate that the addition of thermal noise has the effect of tightening the constraints on the remaining noise parameters, required to show quantum advantage. Furthermore, we show that there exist a threshold temperature at which any quantum sampling experiment becomes classically simulable, and provide an intuitive physical interpretation by relating this occurrence with the disappearance of the quantum state's non-classical properties.