Abstract

We explore the possibility of efficient classical simulation of linear optics experiments in the presence of particle losses. Specifically, we investigate the canonical boson sampling scenario in which an n-particle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors in the m output modes. We examine two models of losses. Inthe first model a fixed number of particles is lost. We prove that in this scenario the output statistics can be well approximated by an efficient classical simulation, provided that the number of photons that is left grows slower than the square of the initial number of particles. In the second loss model, a fraction of photons is lost as they pass through every beamsplitter in the network. For this model the relevant parameter is s, the smallest number of beamsplitters that any photon traverses as it propagates through the network. We prove that it is possible to approximately simulate the output statistics already if s grows logarithmically with the number of modes m, regardless of the geometry of the network. We believe that our findings put strong limitations on future experimental realizations of quantum supremacy proposals based on boson sampling.