## Paolo Zanardi (20/02/17)

Math Colloquium

### Speaker: Paolo Zanardi, University of Southern California

### Title: Quantum algorithms for topological and geometric analysis of Big Data

Location: V-138 (VR-II)

Time: Monday 20 February at 10:00

### Abstract:

Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. I will discuss quantum machine learning algorithms for calculating Betti numbers – the numbers of connected components, holes and voids – in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis.

Reference: Seth Lloyd, Silvano Garnerone e Paolo Zanardi, Quantum algorithms for topological and geometric analysis of data, Nature Communications 7, 10138 (2016). See also: http://news.mit.edu/2016/quantum-approach-big-data-0125