Noise in BosonSampling and the threshold of efficient classical simulability
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We study the quantum to classical transition in BosonSampling by analysing how N-boson interference is affected by inevitable noise in an experimental setup. We adopt the Gaussian noise model of Kalai and Kindler and relate it to realistic experimental imperfections in BosonSampling. We reveal a connection between noise in BosonSampling and partial distinguishability of bosons, which allows us to prove efficient classical simulability of the noisy BosonSampling model, in the non-collision regime, with the noise amplitude ϵ = Θ(1) as N→∞. On the other hand, using an equivalent representation of the noise as losses of bosons compensated by random (dark) counts of detectors, we prove that the noisy BosonSampling model with noise amplitude ϵ=O(1/N) is as hard to simulate classically as the ideal BosonSampling. We find that the ratio of "noise clicks" (lost bosons compensated by dark counts) to the number of bosons N vanishes as N→∞ in the intermediate regime of noise amplitudes ϵ = ω(1/N) and conjecture that such a noisy BosonSampling is also hard to simulate classically. An extension of the Gaussian noise model beyond the no-collision regime is given, with some of our results preserving their validity. In general, our results reveal how imperfections (noise) in an experimental setup cause transition from quantum to classical behaviour in N-boson interference on a linear unitary network when N≫ 1.
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