Strong Simulation of Linear Optical Processes

TL;DR

This paper introduces an efficient algorithm for simulating linear optical processes, significantly outperforming previous methods in computing output probabilities of photons in interferometers, with added versatility for various simulation scenarios.

Contribution

The authors present a novel algorithm that improves simulation efficiency for linear optical processes, outperforming permanent-based methods and enabling hybrid and multiple-input state simulations.

Findings

Algorithm has time complexity linear in output states

Outperforms permanent-based methods exponentially

Supports hybrid sampling and multiple input states

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 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.