Classical simulation of boson sampling with sparse output

Abstract

Boson sampling can simulate physical problems for which classical simulations are inefficient. However, not all problems simulated by boson sampling are classically intractable. We show explicit methods of classically simulating boson sampling when its outcome is known to be highly sparse. In the methods, we first determine a few marginal distributions and then recover the joint distribution from them. Although the latter could be of high complexity in general, we show that it can be classically calculable when the high sparsity assumption holds. Various extensions are discussed including a version involving quantum annealing.

Classical simulation of linear optics subject to nonuniform losses

“…Since the original proposal several small-scale boson sampling experiments have been reported [4][5][6][7][8][9][10][11][12][13][14][15], with state-ofthe-art ranging up to five photons with near-deterministic quantum dot sources [12][13][14]. From the opposite end, there has also been intense activity in the development of classical simulation algorithms [16][17][18], and current supercomputers are expected to simulate 50-photon experiments without much difficulty [17,19]. A more refined analysis of the complexity-theoretic arguments underpinning boson sampling has suggested 90 photons as a concrete milestone for the demonstration of quantum computational advantage [20].…”