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Preprints, Working Papers, ... Year : 2022

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 $O\left({n\binom{n+m-1}{m-1}}\right)$, linear in the number of output states $\binom{n+m-1}{m-1}$. It outperforms the na\"ive 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 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.

Dates and versions

hal-03936315 , version 1 (12-01-2023)

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Nicolas Heurtel, Shane Mansfield, Jean Senellart, Benoît Valiron. Strong Simulation of Linear Optical Processes. 2023. ⟨hal-03936315⟩
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