Simulability of Imperfect Gaussian and Superposition Boson Sampling

TL;DR

This paper investigates the classical simulability of Gaussian and superposition boson sampling under photon distinguishability, revealing conditions under which they become efficiently simulable or remain hard.

Contribution

It demonstrates that distinguishability leads to efficient classical simulation of Gaussian boson sampling and introduces superposition boson sampling as a potentially hard variant.

Findings

Distinguishability causes exponential decay of interference terms in Gaussian boson sampling.

Classical simulation becomes efficient with distinguishability, barring unresolved matrix permanent problems.

Superposition boson sampling shows noise sensitivity and potential computational hardness at zero distinguishability.

Abstract

We study the hardness of classically simulating Gaussian boson sampling at nonzero photon distinguishability. We find that similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference terms in Gaussian boson sampling. Barring an open problem in the theory of matrix permanents, this leads to an efficient classical algorithm to simulate Gaussian boson sampling in the presence of distinguishability. We also study a new form of boson sampling based on photon number superposition states, for which we also show noise sensivity. The fact that such superposition boson sampling is not simulable with out method at zero distinguishability is the first evidence for the computational hardness of this problem.