Data-driven strategies are responsible for the tremendous advances in many fields such as pattern recognition, where the classification algorithm is directly “learnt” from data rather than being built via human-designed mathematical models. Quantum machine learning is a rapidly evolving new discipline that applies data-driven strategies to the quantum realm, where faster algorithms and more accurate estimation methods are theoretically available. Nonetheless, much theoretical work is still needed to understand how to deal with genuinely quantum features, such as entanglement, the no-cloning theorem, and the destructive role of quantum measurements, for machine learning applications. In this seminar I will first review a few selected learning problems in the quantum world , which possibly exploit the computational capabilities offered by current-generation quantum computers , and then discuss how to use tools from quantum information theory and quantum many-body physics to explain the power of quantum machine learning models. Does the model generalize? This is the main question in any data-driven strategy, namely the ability to make predictions about previously unseen data. In Ref.  we have shown that the generalization error can be bounded by entropic quantities, based on the Renyi quantum mutual information. Loosely speaking, our theorem shows using quantitative arguments that a quantum classifier generalizes well when it is capable of discarding as much as possible of the information that is unnecessary to predict the data labels.I will then discuss some applications of our theoretical predictions, such as learning to classify the quantum phasesof an Ising spin chain, or the others shown in Fig. 1. I will also discuss some fundamental properties of “quantum data”, introducing a quantum version of the bias-variance trade-off (a fundamental result in statistical learning theory), and deriving new algorithms, such as what we call thevariational quantum information bottleneck principle.
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 J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
 L. Banchi, J. Pereira, and S. Pirandola, Generalization in quantum machine learning: A quantum information standpoint, PRX Quantum 2, 040321 (2021).