  Topological data analysis offers a robust way to extract useful information
from noisy, unstructured data by identifying its underlying structure.
Recently, an efficient quantum algorithm was proposed [Lloyd, Garnerone,
Zanardi, Nat. Commun. 7, 10138 (2016)] for calculating Betti numbers of data
points -- topological features that count the number of topological holes of
various dimensions in a scatterplot. Here, we implement a proof-of-principle
demonstration of this quantum algorithm by employing a six-photon quantum
processor to successfully analyze the topological features of Betti numbers of
a network including three data points, providing new insights into data
analysis in the era of quantum computing.
