Strong simulation of linear optical processes

In this paper, we provide an algorithm and general framework for the simulation of photons passing through linear optical interferometers. Given n photons at the input of an m-mode interferometer, our algorithm computes the probabilities of all possible output states with time complexity O n(n+m-1 , linear in the number of output states (n+m-1 ?. It outperforms the permanent-based method by an exponential factor, and for the restricted problem of computing the probability for one given output it improves the time complexity over the state-of-the-art for the permanent of matrices with multiple rows or columns, with a tradeoff in the memory usage. Our algorithm also has additional versatility by virtue of its use of memorisation - the storing of intermediate results - which is advantageous in situations where several input states may be of interest. Additionally it allows for hybrid simulations, in which outputs are sampled from output states whose probability exceeds a given threshold, or from a restricted set of states. We consider a concrete, optimised implementation, and we benchmark the efficiency of our approach compared to existing tools.