On Learning Finite-State Quantum Sources

TL;DR

This paper investigates the complexity of learning distributions from finite-state quantum sources, showing that while it is information-theoretically feasible with polynomial samples, it remains computationally hard akin to learning noisy parities.

Contribution

It adapts techniques from hidden Markov models to quantum generators, revealing the computational hardness of learning such quantum distributions.

Findings

Polynomial samples suffice for distribution identification

Computational hardness matches that of learning noisy parities

Bridges quantum learning with classical computational complexity

Abstract

We examine the complexity of learning the distributions produced by finite-state quantum sources. We show how prior techniques for learning hidden Markov models can be adapted to the quantum generator model to find that the analogous state of affairs holds: information-theoretically, a polynomial number of samples suffice to approximately identify the distribution, but computationally, the problem is as hard as learning parities with noise, a notorious open question in computational learning theory.