# Demonstration of Topological Data Analysis on a Quantum Processor

arXiv: https://arxiv.org/abs/1801.06316 · HTML: https://mlsanity.com/paper/1801.06316/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2018.

## Built on by (most cited first, 2 of 2)

- [Active Learning on a Programmable Photonic Quantum Processor](https://mlsanity.com/paper/2208.02104/) (2022)
- [Parameter-Parallel Distributed Variational Quantum Algorithm](https://mlsanity.com/paper/2208.00450/) (2022)

## Abstract (arXiv)

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.