Quantum algorithms for topological and geometric analysis of data
Seth Lloyd, Silvano Garnerone & Paolo Zanardi
Affiliations Contributions Corresponding author
Nature Communications 7, Article number: 10138 doi:10.1038/ncomms10138
Received 17 September 2014 Accepted 09 November 2015 Published 25 January 2016
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. Here we present 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.
Subject terms: Physical sciences Theoretical physics
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