Noise sensitivity of Boson Sampling and density of bosons
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Inevitable experimental noise lies on the way to demonstrate the computational advantage of quantum devices over digital computers in some specific tasks. One of the proposals is Boson Sampling of Aaronson & Arkhipov, where the specific classically hard task is sampling from the many-body quantum interference of N indistinguishable single bosons on a M-dimensional unitary network. Can a noisy realisation of Boson Sampling be efficiently and faithfully simulated classically? We consider how the output distribution of noisy Boson Sampling can be distinguished from that of classical simulation accounting for the many-body interference only up to a fixed order. It is shown that one can distinguish the output distribution of noisy Boson Sampling from that of classical simulation with a number of samples that depends solely on the highest order of quantum interference accounted for by the classical simulation, noise amplitude, and density of bosons ρ = N/M. The results indicate that noisy Boson Sampling in a regime of finite density of bosons, ρ= Θ(1), i.e., on a small network M = N/ρ, retains quantum advantage over digital computers if the amplitude of noise remains bounded as N scales up.
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