On the quantum versus classical learnability of discrete distributions

Sweke R, Seifert JP, Hangleiter D, Eisert J (2021)

Publication Type: Journal article

Publication year: 2021


Book Volume: 5

Article Number: A2

DOI: 10.22331/Q-2021-03-23-417


Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown discrete probability distribution, output with high probability an efficient algorithm for generating new samples from a good approximation of the original distribution. Our primary result is the explicit construction of a class of discrete probability distributions which, under the decisional Diffe-Hellman assumption, is provably not efficiently PAC learnable by a classical generative modelling algorithm, but for which we construct an efficient quantum learner. This class of distributions therefore provides a concrete example of a generative modelling problem for which quantum learners exhibit a provable advantage over classical learning algorithms. In addition, we discuss techniques for proving classical generative modelling hardness results, as well as the relationship between the PAC learnability of Boolean functions and the PAC learnability of discrete probability distributions.

Involved external institutions

How to cite


Sweke, R., Seifert, J.-P., Hangleiter, D., & Eisert, J. (2021). On the quantum versus classical learnability of discrete distributions. Quantum, 5. https://doi.org/10.22331/Q-2021-03-23-417


Sweke, Ryan, et al. "On the quantum versus classical learnability of discrete distributions." Quantum 5 (2021).

BibTeX: Download