The Quantum Learning Menagerie (A survey on Quantum learning for Classical concepts)

TL;DR

This survey reviews quantum learning theory for classical concepts within the PAC framework, highlighting complexity separations and unresolved open problems in the field.

Contribution

It consolidates existing results on quantum versus classical learning complexities and emphasizes the current gaps and open challenges in the area.

Findings

Quantum learning can outperform classical in certain query and sample complexities.

There are significant gaps in understanding the limits of quantum learning for classical concepts.

The paper identifies 23 open problems to guide future research.

Abstract

This paper surveys various results in the field of Quantum Learning theory, specifically focusing on learning quantum-encoded classical concepts in the Probably Approximately Correct (PAC) framework. The cornerstone of this work is the emphasis on query, sample, and time complexity separations between classical and quantum learning that emerge under learning with query access to different labeling oracles. This paper aims to consolidate all known results in the area under the above umbrella and underscore the limits of our understanding by leaving the reader with 23 open problems.