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Quantum Machine Learning
Quantum algorithms for topological and geometric analysis of big data
arXiv
Authors: Seth Lloyd, Silvano Garnerone, Paolo Zanardi
Year
2014
Paper ID
48073
Status
Preprint
Abstract Read
~2 min
Abstract Words
94
Citations
N/A
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.
Why This Paper Matters
- This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
- It adds a 2014 reference point for readers tracking recent quantum research.
- Extracting useful information from large data sets can be a daunting task.
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