Parametric t-stochastic neighbor embedding with quantum neural network

• Published in: Physical review research 2022-12, Vol.4 (4), p.043199, Article 043199
• Main Authors: Kawase, Yoshiaki, Mitarai, Kosuke, Fujii, Keisuke
• Format: Article
• Language: English
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.4.043199

t-stochastic neighbor embedding (t-SNE) is a nonparametric data visualization method in classical machine learning. It maps the data from the high-dimensional space into a low-dimensional space, especially a two-dimensional plane, while maintaining the relationship or similarities between the surrounding points. In t-SNE, the initial position of the low-dimensional data is randomly determined, and the visualization is achieved by moving the low-dimensional data to minimize a cost function. Its variant called parametric t-SNE uses neural networks for this mapping. In this paper, we propose to use quantum neural networks for parametric t-SNE to reflect the characteristics of high-dimensional quantum data on low-dimensional data. We use fidelity-based metrics instead of Euclidean distance in calculating high-dimensional data similarity. To verify our proposed method, we visualize both classical (Iris dataset) and quantum (time-depending Hamiltonian dynamics) data for classification tasks. Since this method allows us to represent a quantum dataset in a higher dimensional Hilbert space by a quantum dataset in a lower dimension while keeping their similarity, the proposed method can also be used to compress quantum data for further quantum machine learning.