Quantum Topological Data Analysis: Accelerating Homology Computation for Complex Data Manifolds
Year: 2025
Type: article
Abstract: : Quantum Topological Data Analysis (QTDA) is introduced as a hybrid classical–quantum methodology for accelerating persistent homology on complex manifolds while preserving topological interpretability. The approach encodes simplicial complexes into quantum states, applies boundary operators via unitary transforms, and estimates invariants with variational and linear‑algebraic quantum routines. An end‑to‑end pipeline is formalized that couples deep representation learning with quantum‑assisted homological primitives, yielding stable persistence diagrams aligned with structural robustness. Experiments on synthetic and semi‑synthetic filtrations quantify latency, scaling, and stability, showing empirical reductions in runtime growth under modest qubit budgets. The results indicate that QTDA enables time‑critical analytics such as anomaly detection and manifold clustering, while meeting explainability and governance requirements through auditable topological summaries. Keywords Quantum Topological Data Analysis, persistent homology, Betti numbers, simplicial complexes, variational quantum algorithms, manifold learning, interpretability, auditability
Author: Murali Krishna Pasupuleti
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4415107664
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