Quantum algorithms for topological and geometric analysis of big data

Understand

Extracting useful information from large data sets can be a daunting task.

• Topological methods for analyzing data sets provide a powerful technique for extracting such information.
• Persistent homology is a sophisticated tool for identifying such topological features -- connected components, holes, or voids -- and for determining how such features persist as the data is viewed at different scales.
• This paper provides quantum algorithms for calculating Betti numbers in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian.