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arXiv:1408.3106quant-ph

Quantum algorithms for topological and geometric analysis of big data

Seth Lloyd, Silvano Garnerone, Paolo Zanardi

Abstract

Extracting useful information from large data sets can be a daunting task. Topological methods for analyzing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying such topological features -- connected components, holes, or voids -- and for determining how such features persist as the data is viewed at different scales. This paper provides quantum algorithms for calculating Betti numbers in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speedup over classical algorithms for topological data analysis.

arXiv comments
20 pages, plain TeX
Journal reference
DOI
Subjects
quant-phQuantum Physics

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Discussed in comments3 threads

  1. Quantum computers: 10-fold boost in stability achieved 1 comment

    • While the OP is wrong about being able to "do everything in parallel" via quantum superposition (we have plenty of no-go theorems when it comes to quantum computers being faster simply due to parallelization) some interesting algorithms that are relevant to data science in…

      johncolanduoniView on HNParent context

  2. Combining topology and quantum computing = huge analysis of data sets 1 comment

    • The actual abstract from http://www.nature.com/ncomms/2016/160125/ncomms10138/abs/nco...: "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.…

      GFK_of_xmaspastView on HNParent context

  3. Microsoft’s Quantum Mechanics 1 comment

    • This one is good too: "Quantum algorithms for topological and geometric analysis of big data" http://arxiv.org/abs/1408.3106 It uses some of this "applied topology", which I only recently found out about. http://www.math.upenn.edu/~ghrist/notes.html

      mathgeniusView on HNParent context

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