Magic in quantum machine learning

A common quantum machine learning paradigm is to use the quantum computer to perform non-linear transformations of input data, as seen in methods like quantum neural networks, quantum kernels, and quantum reservoirs. These transformations can involve either adjustable parametric circuits or fixed circuits followed by classical learning algorithms, such as support vector machines, but in all cases, the quantum computer's role is essentially limited to transforming input data. A natural and critical question is whether these quantum transformations can generate output features that are both inaccessible efficiently to classical methods and beneficial to the learning process. In attempting to answer this question, we explore the relationship between magic and entropy of quantum transformations and their relevance to the generalisation capabilities of the learning model. We show, in a specific scenario, that high-magic circuits tend to produce lower-entropy transformations, suggesting that magic may serve as a valuable resource in quantum machine learning.