Quantum advantage with noisy boson sampling and density of bosons
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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