Quantum algorithms for topological and geometric analysis of data.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 26806491.
- Also identified by DOI 10.1038/ncomms10138 and PMC identifier 4737711.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
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.