# Classical simulation of photonic linear optics with lost particles. (arXiv:1801.06166v1 [quant-ph])

We explore the possibility of efficient classical simulation of linear optics

experiments under the effect 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. In the 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 $\sqrt{n}$. In the second loss model, every time a photon passes

through a beamsplitter in the network, it has some probability of being lost.

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 $m$, regardless of the geometry of

the network. The latter result is obtained by proving that it is always

possible to commute $s$ layers of uniform losses to the input of the network

regardless of its geometry, which could be a result of independent interest. We

believe that our findings put strong limitations on future experimental

realizations of quantum computational supremacy proposals based on boson

sampling.