Demonstration of Topological Data Analysis on a Quantum Processor

Topological data analysis offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. Recently, a quantum algorithm was proposed [Lloyd, Garnerone, Zanardi, Nat. Commun. 7, 10138 (2016)] that can in principle offer an exponential speedup over existing classical algorithms for calculating Betti numbers -- the number of topological holes in a structure at various dimensions. 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.