Machine Learning Class Numbers of Real Quadratic Fields

We implement and interpret various supervised learning experiments involving real quadratic fields with class numbers 1, 2 and 3. We quantify the relative difficulties in separating class numbers of matching/different parity from a data-scientific perspective, apply the methodology of feature analysis and principal component analysis, and use symbolic classification to develop machine-learned formulas for class numbers 1, 2 and 3 that apply to our dataset.

Predict better with less training data using a QNN

Over the past decade, machine learning revolutionized vision-based quality assessment for which convolutional neural networks (CNNs) have now become the standard. In this paper, we consider a potential next step in this development and describe a quanvolutional neural network (QNN) algorithm that efficiently maps classical image data to quantum states and allows for reliable image analysis. We practically demonstrate how to leverage quantum devices in computer vision and how to introduce quantum convolutions into classical CNNs. Dealing with a real world use case in industrial quality control, we implement our hybrid QNN model within the PennyLane framework and empirically observe it to achieve better predictions using much fewer training data than classical CNNs. In other words, we empirically observe a genuine quantum advantage for an industrial application where the advantage is due to superior data encoding.