Free Fermion Distributions Are Hard to Learn
Abstract
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.
Keywords
Cite
@article{arxiv.2306.04731,
title = {Free Fermion Distributions Are Hard to Learn},
author = {Alexander Nietner},
journal= {arXiv preprint arXiv:2306.04731},
year = {2024}
}
Comments
Changes in v2: - Clearer interpretation of Inf. Theorem 1 in terms of the free fermion formalism --> Corollary 7 - Added more background in particular regarding [AG23] - Added discussion about potential average-case generalizations using the results from [Nie23] and [DGK+23]