Inductive supervised quantum learning

TL;DR

This paper explores the fundamental differences and similarities between classical and quantum inductive supervised learning, establishing a quantum de Finetti theorem for channels and analyzing the asymptotic behavior of quantum learning protocols.

Contribution

It introduces a quantum de Finetti theorem for channels and demonstrates the asymptotic equivalence of classical and quantum inductive learning.

Findings

Classical inductive learning naturally follows from non-signalling principles.

Quantum information properties differ from classical, affecting learning equivalence.

Asymptotically, quantum learning protocols resemble classical ones, enabling similar theoretical analysis.

Abstract

In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being non-signalling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from the properties of classical information that break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting, that is, for large number of test instances. This reveals a natural analogy between classical learning protocols and their quantum counterparts, justifying a similar treatment, and allowing to inquire about standard elements in computational learning theory, such as structural risk minimization and sample complexity.