Quantum Computing and Persistence in Topological Data Analysis

Explore the intersection of quantum computing and topological data analysis in this 34-minute conference talk from QTML 2025. Learn how quantum algorithms can provide exponential speedups for determining hole persistence across different length scales in topological data analysis. Discover the theoretical foundations showing that deciding whether a given hole persists is BQP₁-hard and contained in BQP, establishing quantum computational advantages under standard complexity-theoretic assumptions. Examine how hole persistence can be encoded through the guided sparse Hamiltonian problem, with guiding states constructed from harmonic representatives of holes. Gain insights into cutting-edge research connecting quantum complexity theory with robust feature extraction methods in data analysis, presented by researchers from leading quantum computing institutions.