Strong Simulation of Linear Optical Processes

Abstract

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, linear in the number of output states n+m−1 m−1 . It outperforms the naïve method by an exponential factor, and for the restricted problem of computing the probability for one given output it matches the current state-of-the-art. Our algorithm also has additional versatility by virtue of its use of memorisationthe 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.

Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing

“…The SLOS Back-end. The Strong Linear Optical Simulation SLOS algorithm developed by a subset of the present authors is introduced in [45]. It unfolds the full computation path in memory, leading to a remarkable time complexity of O n m+n−1 n for computing the full distribution.…”

“…The current implementation also allows restrictive sets of outputs, with average computing time in O(nρ n θ ) for single output computation. As discussed in [45], it is possible to use the SLOS algorithm in a hybrid manner that can combine both weak and strong simulation, though it has not yet been implemented in the current version of Perceval . The tradeoff in the SLOS algorithm is a huge memory usage of O n m+n−1 n that limits usage to circuits with ≈ 20 photons on personal computers and with ≈ 24 photons on super-computers.…”