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Predictive Quantum Learning

We demonstrate a relational concept class that is efficiently learnable in certain quantum analogue of the PAC model, while in any classical learning model exponential amount of training data would be required. We show that our separation is the best possible in several ways; in particular, there is no analogous result for a functional class, as well as for some weaker versions of quantum PAC. This is the first (unconditional) separation of quantum and classical learning models.