Quantum topological data analysis with continuous variables

TL;DR

This paper presents a quantum algorithm using continuous variables and qRAM to compute Betti numbers in persistent homology, advancing quantum topological data analysis techniques.

Contribution

It introduces a novel continuous-variable quantum algorithm for topological data analysis, utilizing qRAM and phase estimation for Betti number calculation.

Findings

Successfully computes Betti numbers using quantum phase estimation.

Demonstrates the use of continuous-variable quantum gates in topological analysis.

Provides a framework for quantum-enhanced topological data analysis.

Abstract

I introduce a continuous-variable quantum topological data algorithm. The goal of the quantum algorithm is to calculate the Betti numbers in persistent homology which are the dimensions of the kernel of the combinatorial Laplacian. I accomplish this task with the use of qRAM to create an oracle which organizes sets of data. I then perform a continuous-variable phase estimation on a Dirac operator to get a probability distribution with eigenvalue peaks. The results also leverage an implementation of continuous-variable conditional swap gate.