Quantum algorithms for topological and geometric analysis of data
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...
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| Format: | Article |
| Jezik: | en_US |
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Nature Publishing Group
2016
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| Online dostop: | http://hdl.handle.net/1721.1/101739 |
| _version_ | 1826194524734488576 |
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| author | Lloyd, Seth Garnerone, Silvano Zanardi, Paolo |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Lloyd, Seth Garnerone, Silvano Zanardi, Paolo |
| author_sort | Lloyd, Seth |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:57:06Z |
| format | Article |
| id | mit-1721.1/101739 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:57:06Z |
| publishDate | 2016 |
| publisher | Nature Publishing Group |
| record_format | dspace |
| spelling | mit-1721.1/1017392022-09-26T14:49:20Z Quantum algorithms for topological and geometric analysis of data Lloyd, Seth Garnerone, Silvano Zanardi, Paolo Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Research Laboratory of Electronics Lloyd, Seth 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. United States. Army Research Office United States. Air Force Office of Scientific Research United States. Defense Advanced Research Projects Agency 2016-03-18T14:47:34Z 2016-03-18T14:47:34Z 2016-01 2014-09 Article http://purl.org/eprint/type/JournalArticle 2041-1723 http://hdl.handle.net/1721.1/101739 Lloyd, Seth, Silvano Garnerone, and Paolo Zanardi. “Quantum Algorithms for Topological and Geometric Analysis of Data.” Nat Comms 7 (January 25, 2016): 10138. en_US http://dx.doi.org/10.1038/ncomms10138 Nature Communications Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ application/pdf Nature Publishing Group Nature Publishing Group |
| spellingShingle | Lloyd, Seth Garnerone, Silvano Zanardi, Paolo Quantum algorithms for topological and geometric analysis of data |
| title | Quantum algorithms for topological and geometric analysis of data |
| title_full | Quantum algorithms for topological and geometric analysis of data |
| title_fullStr | Quantum algorithms for topological and geometric analysis of data |
| title_full_unstemmed | Quantum algorithms for topological and geometric analysis of data |
| title_short | Quantum algorithms for topological and geometric analysis of data |
| title_sort | quantum algorithms for topological and geometric analysis of data |
| url | http://hdl.handle.net/1721.1/101739 |
| work_keys_str_mv | AT lloydseth quantumalgorithmsfortopologicalandgeometricanalysisofdata AT garneronesilvano quantumalgorithmsfortopologicalandgeometricanalysisofdata AT zanardipaolo quantumalgorithmsfortopologicalandgeometricanalysisofdata |