Quantum-Enhanced Topological Data Analysis: A Peep from an Implementation Perspective

TL;DR

This paper presents a detailed implementation of a quantum algorithm for Topological Data Analysis, specifically calculating Betti numbers, and explores its application in machine learning with preliminary experimental insights.

Contribution

It provides the first comprehensive implementation guide for a quantum TDA algorithm and discusses its practical use in machine learning tasks.

Findings

Successful implementation of Betti number calculation on quantum hardware

Betti numbers can be used for classification tasks

Preliminary analysis shows the impact of shots and qubits on results

Abstract

There is heightened interest in quantum algorithms for Topological Data Analysis (TDA) as it is a powerful tool for data analysis, but it can get highly computationally expensive. Even though there are different propositions and observations for Quantum Topological Data Analysis (QTDA), the necessary details to implement them on software platforms are lacking. Towards closing this gap, the present paper presents an implementation of one such algorithm for calculating Betti numbers. The step-by-step instructions for the chosen quantum algorithm and the aspects of how it can be used for machine learning tasks are provided. We provide encouraging results on using Betti numbers for classification and give a preliminary analysis of the effect of the number of shots and precision qubits on the outcome of the quantum algorithm.