Quantum algorithms for topological and geometric analysis of data

Nature Communications
Seth LloydPaolo Zanardi

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.

References

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Citations

Feb 13, 2018·Proceedings. Mathematical, Physical, and Engineering Sciences·Carlo CilibertoLeonard Wossnig
Mar 6, 2018·Reports on Progress in Physics·Vedran Dunjko, Hans J Briegel
Sep 15, 2017·Nature·Jacob BiamonteSeth Lloyd
Nov 18, 2016·Royal Society Open Science·Allen D Parks, David J Marchette
Sep 5, 2019·Scientific Reports·Laszlo Gyongyosi, Sandor Imre
May 3, 2019·Scientific Reports·Laszlo Gyongyosi, Sandor Imre
Jul 10, 2020·Scientific Reports·Laszlo Gyongyosi, Sandor Imre
Jan 25, 2020·Physical Review Letters·Dan-Bo ZhangZ D Wang
May 27, 2017·Physical Review Letters·Alex MonràsPeter Wittek
Jul 3, 2020·Scientific Reports·Laszlo Gyongyosi
Aug 20, 2021·Science Advances·Zhaokai LiJiangfeng Du
May 15, 2017··Nathan WiebeMartin Roetteler

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Software Mentioned

qRAM

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