IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v7y2016i1d10.1038_ncomms10138.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/ncomms10138
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1038/ncomms10138?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    4. Marcos Crichigno & Tamara Kohler, 2024. "Clique Homology is $${{\mathsf{QMA}}}_{1}$$ QMA 1 -hard," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
    5. Muolo, Riccardo & Carletti, Timoteo & Bianconi, Ginestra, 2024. "The three way Dirac operator and dynamical Turing and Dirac induced patterns on nodes and links," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms10138. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.nature.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.