Free fermions are some of the best studied quantum systems. However, little is known about the complexity of learning free-fermion distributions. In this work we establish the hardness of this task in the particle number non-preserving case. In particular, we give an information theoretical hardness result for the general task of learning from expectation values and, in the more general case when the algorithm is given access to samples, we give a computational hardness result based on the LPN assumption for learning the probability density function.

翻译：自由费米子是最受研究的量子系统之一。然而，关于学习自由费米子分布的复杂性却鲜为人知。本文证明了在粒子数不守恒情形下该任务的难度。具体而言，我们针对从期望值学习的通用任务给出了信息论层面的难度结论；而在算法可获取样本的更一般情形中，我们基于LPN假设给出了学习概率密度函数的计算复杂性难度结论。