Distinguishing noisy boson sampling from classical simulations

TL;DR

This paper demonstrates that it is possible to efficiently distinguish noisy boson sampling outputs from classical approximations, with the required samples depending critically on the boson density, advancing the understanding of quantum supremacy verification.

Contribution

The work analytically and numerically shows how to differentiate noisy boson sampling from classical simulations, highlighting the role of boson density in this distinction.

Findings

Distinguishing noisy boson sampling from classical algorithms is feasible.

Sample complexity depends strongly on boson density.

Critical density effects resemble quantum-to-classical transition phenomena.

Abstract

Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise. Recently found classical algorithms can efficiently approximate, to any small error, the output of boson sampling with finite-amplitude noise. In this work it is shown analytically and confirmed by numerical simulations that one can efficiently distinguish the output distribution of such a noisy boson sampling from the approximations accounting for low-order quantum multiboson interferences, what includes the mentioned classical algorithms. The number of samples required to tell apart the quantum and classical output distributions is strongly affected by the previously unexplored parameter: density of bosons, i.e., the ratio of total number of interfering bosons to number of input ports of interferometer. Such critical dependence is strikingly reminiscent of the quantum-to-classical transition in systems of identical particles, which sets in when the system size scales up while density of particles vanishes.