Quantum-Enhanced Anomaly Explanation: Interpretable TDA for Outlier Attribution

Building on Pasupuleti (2025)’s Quantum Topological Data Analysis (QTDA), which demonstrated speedups in persistent homology for anomaly detection, this idea goes a step further by directly linking anomalous data points to specific topological generators (e.g., which cycles or voids caused the anomaly score to spike). While current QTDA approaches focus on runtime and robustness, they stop short of providing human-interpretable attributions for anomalies. By coupling quantum persistent homology with the interpretability framework proposed by Debnath et al. (2025), this research would create a transparent diagnosis pipeline: quantum routines detect anomalies, and post-hoc analysis traces back the “culprit” homological features. This could revolutionize anomaly detection in fields like finance and cybersecurity, where understanding why something is anomalous is as important as detecting it in the first place.

References:

1. Quantum Topological Data Analysis: Accelerating Homology Computation for Complex Data Manifolds. Murali Krishna Pasupuleti (2025). International Journal of Academic and Industrial Research Innovations(IJAIRI).
2. Mathematical Foundations of Explainable AI: A Framework based on Topological Data Analysis. Mintu Debnath, Vijay Kumar Salvia, Alighazi Siddiqui, Khalid Ali Qidwai, P. Durga, S. Bavankumar (2025). Communications on Applied Nonlinear Analysis.