Geometric Quantum Machine Learning

Recognizing the underlying symmetries in a given dataset has recently played a fundamental role in classical machine learning, leading to the burgeoning field of geometric deep learning. Some of the ideas of geometric deep learning have been imported into the field of quantum machine learning, leading to a novel field that has been termed geometric quantum machine learning (GQML). In this talk, we will review the basic concepts of GQML. We will begin with a comprehensive introduction to the necessary tools from representation theory to understand and manipulate symmetries in the dataset. Then, we will show how to create models encoding the symmetries of the learning task. This is materialized through the usage of equivariant neural networks whose action commutes with that of the symmetry. Finally, we will show how equivariant quantum neural networks can solve many of the critical issues in variational quantum machine learning. In particular, we will prove that permutation-equivariant architectures do not suffer from barren plateaus, quickly reach overparametrization, and can generalize well from small amounts of data.