  We give an efficient algorithm that learns a non-interacting fermion state,
given copies of the state. For a system of $n$ non-interacting fermions and $m$
modes, we show that $O(m^3 n^2 \log(1/\delta) / \epsilon^4)$ copies of the
input state and $O(m^4 n^2 \log(1/\delta)/ \epsilon^4)$ time are sufficient to
learn the state to trace distance at most $\epsilon$ with probability at least
$1 - \delta$. Our algorithm empirically estimates one-mode correlations in
$O(m)$ different measurement bases and uses them to reconstruct a succinct
description of the entire state efficiently.
