Quantum computing, a discipline that investigates how computing changes if we take into account quantum effects, has turned into an emerging technology that produced the first generation of hardware prototypes. In search of applications for these new devices, researchers turned to machine learning and found a wealth of exciting questions: Do machine learning algorithms gain a better computational complexity if we outsource parts of them to quantum computers? How does the problem of empirical risk minimisation change if our model class is made up of quantum algorithms? How does quantum hardware fit into AI pipelines? And, vice versa, can machine learning help us to study the behaviour of quantum systems?

In this tutorial we want to unpack these questions and sketch the landscape of preliminary answers found so far. For example, we will look at carefully constructed learning problems for which quantum computers have a provable complexity advantage, and motivate why it is so hard to make conclusive statements about more natural problem settings. We will explore how data can be represented as physical states of quantum systems, and how manipulating these systems leads to algorithms that are just kernel methods with a special kind of Hilbert space. We will see that quantum devices can be trained like neural networks, and that existing open-source software seamlessly integrates them into deep learning pipelines. Finally, we will understand how the deep connections between neural networks and quantum wave functions allow us to use machine learning techniques to understand quantum systems themselves.

The tutorial targets a broad audience, and no prior knowledge of physics is required.