Understanding the Mapping of Encode Data Through An Implementation of Quantum Topological Analysis

Abstract

Topological Data Analysis (TDA) is a well-established field derived to give insight into the geometric structure of real-world data. However, many methods in TDA are computationally intensive. The method that computes the respective Betti number has been shown to obtain a speed-up from translating the algorithm into a quantum circuit. The quantum circuit to calculate a particular Betti number requires a significant number of gates and, without a small record of data, is currently unable to be implemented on a NISQ-era processor. Given this NISQ-era restriction, a hybrid-method is proposed that calculates the Euclidean distance of the encoded data and computes the desired Betti number. This method is applied to a toy data set with different encoding techniques. The empirical results show the noise within the data is intensified with each encoding method as there is a clear change in the geometric structure of the original data, exhibiting information loss.