Demonstration of Topological Data Analysis on a Quantum Processor

TL;DR

This paper demonstrates a quantum algorithm for topological data analysis by implementing it on a six-photon quantum processor to analyze Betti numbers of a small data network, showcasing quantum computing's potential in data analysis.

Contribution

It provides the first experimental demonstration of a quantum algorithm for topological data analysis using photonic quantum processors.

Findings

Successful analysis of Betti numbers of a three-point network

First proof-of-principle quantum implementation of topological data analysis

Shows potential for quantum computing in complex data structure analysis

Abstract

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.