Prof. Dr. Dr. h.c. Frank Leymann: “Quantum Topological Data Analysis”

In this lecture we introduce the fundamental concept of homology as the basis of topological data analysis. Based on this, Betti numbers are introduced as characteristic quantities and it is shown how to calculate them. In order to analyse a data set, its persistent homology is calculated: for this purpose, the corresponding point sets are transformed into simplicial complexes in a scaled manner. Finally, we will outline how quantum algorithms can compute Betti numbers exponentially faster than classically (even on NISQ machines) and why we believe we will soon be able to prove a quantum advantage here.

Target group: Advanced (This talk is very mathematical)