Quaternion-based machine learning on topological quantum systems
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 archit...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2023-01-01
|
| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/acc0d6 |
| _version_ | 1797844625694654464 |
|---|---|
| author | Min-Ruei Lin Wan-Ju Li Shin-Ming Huang |
| author_facet | Min-Ruei Lin Wan-Ju Li Shin-Ming Huang |
| author_sort | Min-Ruei Lin |
| collection | DOAJ |
| description | 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 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 distributions 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. |
| first_indexed | 2024-04-09T17:25:21Z |
| format | Article |
| id | doaj.art-ce8e3dec17484e3d9dac0d0824b8d6f4 |
| institution | Directory Open Access Journal |
| issn | 2632-2153 |
| language | English |
| last_indexed | 2024-04-09T17:25:21Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj.art-ce8e3dec17484e3d9dac0d0824b8d6f42023-04-18T13:52:36ZengIOP PublishingMachine Learning: Science and Technology2632-21532023-01-014101503210.1088/2632-2153/acc0d6Quaternion-based machine learning on topological quantum systemsMin-Ruei Lin0Wan-Ju Li1https://orcid.org/0000-0002-1797-8481Shin-Ming Huang2https://orcid.org/0000-0003-4273-9682Department of Physics, National Sun Yat-sen University , Kaohsiung 80424, Taiwan; Department of Applied Mathematics, National Sun Yat-sen University , Kaohsiung 80424, TaiwanDepartment of Physics, National Sun Yat-sen University , Kaohsiung 80424, TaiwanDepartment of Physics, National Sun Yat-sen University , Kaohsiung 80424, Taiwan; Physics Division, National Center for Theoretical Sciences , Taipei 10617, TaiwanTopological 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 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 distributions 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.https://doi.org/10.1088/2632-2153/acc0d6quaternionconvolutional neural networktopologicalclassificationmachine learningprincipal component analysis |
| spellingShingle | Min-Ruei Lin Wan-Ju Li Shin-Ming Huang Quaternion-based machine learning on topological quantum systems Machine Learning: Science and Technology quaternion convolutional neural network topological classification machine learning principal component analysis |
| title | Quaternion-based machine learning on topological quantum systems |
| title_full | Quaternion-based machine learning on topological quantum systems |
| title_fullStr | Quaternion-based machine learning on topological quantum systems |
| title_full_unstemmed | Quaternion-based machine learning on topological quantum systems |
| title_short | Quaternion-based machine learning on topological quantum systems |
| title_sort | quaternion based machine learning on topological quantum systems |
| topic | quaternion convolutional neural network topological classification machine learning principal component analysis |
| url | https://doi.org/10.1088/2632-2153/acc0d6 |
| work_keys_str_mv | AT minrueilin quaternionbasedmachinelearningontopologicalquantumsystems AT wanjuli quaternionbasedmachinelearningontopologicalquantumsystems AT shinminghuang quaternionbasedmachinelearningontopologicalquantumsystems |