Parametric t-Stochastic Neighbor Embedding With Quantum Neural Network

TL;DR

This paper introduces a novel quantum neural network-based parametric t-SNE method that visualizes high-dimensional quantum data in low-dimensional space, preserving similarities using fidelity metrics, and demonstrates its application on classical and quantum datasets.

Contribution

It proposes integrating quantum neural networks into parametric t-SNE, enabling visualization and compression of quantum data while maintaining data similarities.

Findings

Successfully visualized classical and quantum datasets.

Used fidelity metrics for similarity, improving quantum data representation.

Potential for quantum data compression in quantum machine learning.

Abstract

t-Stochastic Neighbor Embedding (t-SNE) is a non-parametric 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. 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.