Quantum advantage with noisy boson sampling and density of bosons
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Inevitable noise is the main problem in demonstration of computational advantage of quantum devices, such as boson sampling, over digital computers. Can a noisy realization of boson sampling be efficiently and faithfully simulated classically? It is shown how one can distinguish the output distribution of noisy N-boson sampling from that of classical approximations with mixtures of quantum interferences of up to K≪√(N) bosons, with a number of samples that depends solely on K, noise amplitude and density of bosons ρ = N/M, where M is network size. The surprising result is that noisy boson sampling in a regime of finite density of bosons ρ< 1, i.e., on a small network M = N/ρ, retains scalable quantum advantage to arbitrary large number of bosons despite the presence of finite noise.
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