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, an efficient quantum algorithm was proposed [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. (c) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement