Human society is currently generating


on the order of a billion billion (10ˆ18) bits of data a year.

Extracting useful information 
from large data sets can be a daunting task. 
[Not to mention a bit of wisdom...]

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.

Quantum algorithms for topological and geometric analysis of big data
Seth Lloyd [1], Silvano Garnerone [2], Paolo Zanardi [3]

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