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Center for Nonlinear Studies |
Topological Data Analysis (TDA) extracts robust features from data by analyzing the presence and persistence of topological holes. In this talk, I will discuss how a core problem in TDA—determining whether a given hole persists across different length scales—admits a potential super-polynomial quantum speedup. We establish this by showing that the problem is BQP_1-hard and contained in BQP, relying on a connection to a variant of the guided sparse Hamiltonian problem. Our approach encodes the persistence of a hole using a harmonic representative, offering new insights into the computational power of quantum algorithms for TDA.
Bio: I completed my undergraduate studies in Mathematics at the University of Amsterdam before earning a PhD in Quantum Machine Learning at Leiden University under the supervision of Vedran Dunjko. My research interests lie in learning theory, complexity theory and fault-tolerant quantum algorithms for machine learning, with a particular focus on topological data analysis. I am currently a Senior Researcher at Pasqal, a neutral-atom quantum computing company, where I work on fault-tolerant quantum algorithms.
Host: Martin Larocca, T-4/CNLS