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Quantum algorithms for topological and geometric analysis of data

Author

Listed:
  • 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)

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.

Suggested Citation

  • Seth Lloyd & Silvano Garnerone & Paolo Zanardi, 2016. "Quantum algorithms for topological and geometric analysis of data," Nature Communications, Nature, vol. 7(1), pages 1-7, April.
    • Handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms10138
    DOI: 10.1038/ncomms10138
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    Cited by:

    1. Huang, Fangyu & Tan, Xiaoqing & Huang, Rui & Xu, Qingshan, 2022. "Variational convolutional neural networks classifiers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    2. Dylan Herman & Cody Googin & Xiaoyuan Liu & Alexey Galda & Ilya Safro & Yue Sun & Marco Pistoia & Yuri Alexeev, 2022. "A Survey of Quantum Computing for Finance," Papers 2201.02773, arXiv.org, revised Jun 2022.
    3. Fujii, Hidemichi & Managi, Shunsuke, 2018. "Trends and priority shifts in artificial intelligence technology invention: A global patent analysis," Economic Analysis and Policy, Elsevier, vol. 58(C), pages 60-69.

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