Quaternion-based machine learning on topological quantum systems

TL;DR

This paper introduces quaternion algebra into machine learning models to improve the classification of topological phases in quantum systems, demonstrating enhanced feature extraction and classification accuracy.

Contribution

It develops quaternion-based neural networks and PCA methods for topological phase classification, showing advantages over conventional approaches.

Findings

Quaternion PCA distinguishes topological phases effectively.

Quaternion neural networks classify phases even with unseen data distributions.

Quaternion methods outperform traditional techniques in topological classification tasks.

Abstract

Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the complexity in quantum physics, advanced mathematical architecture should be considered in designing machines. In this work, we incorporate quaternion algebras into data analysis either in the frame of supervised and unsupervised learning to classify two-dimensional Chern insulators. For the unsupervised-learning aspect, we apply the principal component analysis (PCA) on the quaternion-transformed eigenstates to distinguish topological phases. For the supervised-learning aspect, we construct our machine by adding one quaternion convolutional layer on top of a conventional convolutional neural network. The machine takes quaternion-transformed configurations as inputs and successfully classify all distinct topological phases, even for those states that have different distributuions from those states seen by the machine during the training process. Our work demonstrates the power of quaternion algebras on extracting crucial features from the targeted data and the advantages of quaternion-based neural networks than conventional ones in the tasks of topological phase classifications.