Depth-Based Matrix Classification for the HHL Quantum Algorithm

TL;DR

This paper explores using machine learning classifiers, specifically Multi-Layer Perceptrons, to predict the suitability of linear systems for the HHL quantum algorithm based on numerical matrix properties.

Contribution

It introduces a method to classify problems as suitable or unsuitable for HHL using ML, emphasizing the importance of representative training data.

Findings

ML classifiers can accurately predict HHL suitability

Training data distribution critically affects classification performance

Multi-Layer Perceptrons outperform other models in this task

Abstract

Under the nearing error-corrected era of quantum computing, it is necessary to understand the suitability of certain post-NISQ algorithms for practical problems. One of the most promising, applicable and yet difficult to implement in practical terms is the Harrow, Hassidim and Lloyd (HHL) algorithm for linear systems of equations. An enormous number of problems can be expressed as linear systems of equations, from Machine Learning to fluid dynamics. However, in most cases, HHL will not be able to provide a practical, reasonable solution to these problems. This paper's goal inquires about whether problems can be labeled using Machine Learning classifiers as suitable or unsuitable for HHL implementation when some numerical information about the problem is known beforehand. This work demonstrates that training on significantly representative data distributions is critical to achieve good classifications of the problems based on the numerical properties of the matrix representing the system of equations. Accurate classification is possible through Multi-Layer Perceptrons, although with careful design of the training data distribution and classifier parameters.