Classification of Linear Systems of Equations for Quantum Computing Implementation

Drawing nearer to an 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 to electrical circuit analysis. However, in most cases, HHL will not be able to provide a practical, reasonable solution to these problems. This work seeks to determine whether problems can be labeled as suitable or unsuitable for HHL implementation using machine learning classifiers when some numerical information about the problem is known beforehand. It is demonstrated that training on a data distribution that is sufficiently representative of the target problem space is critical to achieve good classifications of the problems based on the numerical properties of a system’s coefficient matrix. Accurate classification is possible using multi-layer perceptrons, though only with careful design and selection of the training data distribution and classifier optimizations.