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 $O(m^2 n^4 \log(m/\delta)/ \varepsilon^4)$ samples and $O(m^4 n^4 \log(m/\delta)/ \varepsilon^4)$ time are sufficient to learn the original distribution to total variation distance $\varepsilon$ with probability $1 - \delta$. Our algorithm empirically estimates the one- and two-mode correlations and uses them to reconstruct a succinct description of the entire distribution efficiently.

翻译：我们给出了一个高效的经典算法, 恢复了计算基础上非互动发酵状态的分配。 对于一个非互动发酵和美元模式的系统, 我们显示, 美元( m/\ delta) /\ varepsilon ⁇ 4) 样本和 美元( m/ delta) 4\ log( m/\ delta) /\ varepsilon4) 时间足以学习原始分配到总变差距离$\ varepsilon$( 概率为 $ -\ delta$) 和 美元。 我们的算法根据经验估算了一元和二元相关关系, 并用它们来高效地重建整个分布的简明描述 。