Topological Data Analysis for Complex Quantum Systems

This paper introduces novel applications of topological data analysis (TDA) techniques to characterize and classify complex quantum systems. We leverage persistent homology to extract robust topological features from experimental and simulated data of quantum many-body states, including those exhibiting exotic phases. This approach provides a powerful, coordinate-free method for distinguishing different quantum phases and identifying phase transitions. The implications are significant for quantum materials discovery, quantum sensor development, and the verification of quantum simulations.