This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learn- ing: exact learning from membership queries, and Probably Approximately Correct (PAC) and agnostic learning from classical or quantum examples.

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doi.org/10.1145/3106700.3106710
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Arunachalam, S., & de Wolf, R. (2017). A survey of quantum learning theory. ACM SIGACT News, 48(2), 41–67. doi:10.1145/3106700.3106710