Quaternion-based machine learning on topological quantum systems
- URL: http://arxiv.org/abs/2209.14551v2
- Date: Fri, 5 May 2023 02:00:43 GMT
- Title: Quaternion-based machine learning on topological quantum systems
- Authors: Min-Ruei Lin, Wan-Ju Li, and Shin-Ming Huang
- Abstract summary: In this work, we incorporate quaternion algebras into data analysis to classify two-dimensional Chern insulators.
For the unsupervised-learning aspect, we apply the principal component analysis (PCA) on the quaternion-transformed eigenstates.
We construct our machine by adding one quaternion convolutional layer on top of a conventional convolutional neural network.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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