Quantum Learning Theory Beyond Batch Binary Classification

Abstract

Arunachalam and de Wolf (2018) [1] showed that the sample complexity of quantum batch learning of boolean functions, in the realizable and agnostic settings, has the $\textit{same form and order}$ as the corresponding classical sample complexities. In this paper, we extend this, ostensibly surprising, message to batch multiclass learning, online boolean learning, and online multiclass learning. For our online learning results, we first consider an adaptive adversary variant of the classical model of Dawid and Tewari (2022) [2]. Then, we introduce the first (to the best of our knowledge) model of online learning with quantum examples.