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(m2n4log(m/δ)/ε4) samples and O(m4n4log(m/δ)/ε4) 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.Comment: 7 page