Efficient Learning of Non-Interacting Fermion Distributions

02/20/2021

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by   Scott Aaronson, et al.

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We give an efficient classical algorithm that recovers the distribution of a non-interacting fermion state over the computational basis. For a system of n non-interacting fermions and m modes, we show that O(m^2 n^4 log(m/δ)/ ε^4) samples and O(m^4 n^4 log(m/δ)/ ε^4) time are sufficient to learn the original distribution to total variation distance ε with probability 1 - δ. Our algorithm empirically estimates the one- and two-mode correlations and uses them to reconstruct a succinct description of the entire distribution efficiently.