Learning with Quantum Models

Abstract

The last two chapters were mainly concerned with the translation of known machine learning models and optimisation techniques into quantum algorithms in order to harvest potential runtime speedups known from quantum computing. This chapter will look into ‘genuine’ quantum models for machine learning which either have no direct equivalent in classical machine learning, or which are quantum extensions of classical models with a new quality of dynamics. A quantum model as we understand it here is a model function or distribution that is based on the mathematical formalism of quantum theory, or naturally implemented by a quantum device. For example, it has been obvious from the last chapters that Gibbs distributions play a prominent role in some areas of machine learning. At the same time, quantum systems can be in a ‘Gibbs state’. Previously, we described a number of attempts to use the quantum Gibbs states in order to sample from a (classical) Gibbs distribution. But what happens if we just use the ‘quantum Gibbs distribution’? What properties would such models or training schemes exhibit? What if we use other distributions that are easy to prepare on a quantum device but difficult on a classical one, and construct machine learning algorithms from them? How powerful are the classifiers constructed from variational circuits in Section, that is if we use the input-output relation of a quantum circuit as a core machine learning model f(x) and train the circuit to generalise from data?