Dimensionality reduction is essential for analyzing high-dimensional datasets across various fields. While t-SNE is a popular method for this purpose in Euclidean spaces, recent advancements suggest that hyperbolic spaces can better represent hierarchical structures. However, there is a notable lack of data structures and algorithms tailored for hyperbolic spaces. This research addresses this gap by implementing a hyperbolic quadtree structure in the upper half-plane model and integrating it into the hyperbolic t-SNE framework. Our goal is to accelerate the optimization of the hyperbolic t-SNE while maintaining reasonable precision and recall. We conduct rigorous benchmarking experiments to evaluate the performance of this approach, comparing it to existing methods. The findings provide insights into the practical utility of using the hyperbolic quadtree structure in the upper half-plane model in hyperbolic t-SNE embeddings.