Quantum speedup, circuit decoupling, and stochastic modelling: on how quantum theory improves machine-learning, and how machine-learning helps to process quantum information

Abstract

In today's data-driven society, the importance of data is ever-increasing. The ability to discern patterns and trends in this data allows us to make predictive and informed decisions. This quest for enhanced data analysis has fueled the evolution of machine learning. Quantum Machine Learning (QML) is an emerging field that seeks to amalgamate the power of quantum computing with machine learning. Despite the term quantum in its name, QML is a hybrid approach incorporating both classical and quantum processing. This fusion of classical and quantum processing enables QML to capitalize on the advantages of both. However, this integration also introduces a novel set of challenges. Here we will explore QML from computer science and physics perspectives. In the first part, the mathematical tools for machine learning and quantum theory are introduced. Then the second part will investigate how quantum computation enhances classical machine learning algorithms, with a demonstration of quantum advantages in computational complexity. The third part explores the learning of quantum models through classical optimization methods. We will find how the features of a quantum model can be learned by optimization, and how a quantum model can be trained to generate target stochastic data.