Demonstration of Topological Data Analysis on a Quantum Processor
This is an incremental proof-of-principle demonstration for data analysis in quantum computing, with limited practical impact due to small-scale implementation.
The researchers implemented a quantum algorithm for topological data analysis on a six-photon quantum processor, successfully calculating Betti numbers for a network with three data points to demonstrate its feasibility in quantum computing.
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.