Quantum algorithms for topological and geometric analysis of data

Seth Lloyd (), Silvano Garnerone and Paolo Zanardi
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Seth Lloyd: Research Lab for Electronics, Massachusetts Institute of Technology
Silvano Garnerone: Institute for Quantum Computing, University of Waterloo
Paolo Zanardi: Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089-0484, USA

Nature Communications, 2016, vol. 7, issue 1, 1-7

Abstract: 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.

Date: 2016
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DOI: 10.1038/ncomms10138

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