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]

http://arxiv.org/pdf/1408.3106.pdf