Quantum computing and persistence in topological data analysis

Extracting valuable insights from complex datasets is a ubiquitous challenge in modern data analysis and machine learning. Topological Data Analysis(TDA) [ELZ02, ZC04] has recently gained attention as a powerful method for addressing this challenge by utilizing tools from algebraic topology. Topological data analysis is particularly advantageous due to its robustness against noise and its ability to capture global, higherdimensional topological features, which traditional geometric and graph-based methods often miss [EH22]. In topological data analysis, data is first transformed into a series of combinatorial structures called a filtration of simplicial complexes. A simplicial complex consists of simplices (i.e., points, lines, triangles, tetrahedra, and their higher-dimensional analogs) that are connected or "glued" together.