Quantum algorithms for topological and geometric analysis of data
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Lloyd-2016-Quantum Algorithms.pdf
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220.19 KB
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Author(s)
Lloyd, Seth
Garnerone, Silvano
Zanardi, Paolo
Date Issued
January 2016
Journal
Nature Communications
Publisher
Nature Publishing Group
Citation
Lloyd, Seth, Silvano Garnerone, and Paolo Zanardi. “Quantum Algorithms for Topological and Geometric Analysis of Data.” Nat Comms 7 (January 25, 2016): 10138.
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1038/ncomms10138
