Depth-Based Matrix Classification for the HHL Quantum Algorithm

2025-05-28

AI Summary

To address practical deployment requirements of the HHL algorithm in the post-NISQ era, this work tackles the challenge of pre-assessing whether a given linear system is suitable for quantum solution. Method: We propose the first binary classification paradigm for HHL applicability, grounded in numerical characteristics of the coefficient matrix—including condition number, sparsity, and spectral distribution. A multi-layer perceptron classifier is trained using customized numerical feature engineering and a hybrid sampling strategy combining synthetic and real-world matrices. Crucially, we identify that representativeness of the training data distribution fundamentally governs model robustness. Results: Evaluated across diverse matrix benchmarks, our classifier achieves over 92% accuracy, significantly improving the efficiency of feasibility assessment prior to quantum algorithm execution. The framework provides an interpretable, scalable, and quantum-classical co-design–ready evaluation tool for the fault-tolerant era.

Technology Category

• Machine Learning: Quantum Machine Learning
• Humans and AI: Human-in-the-loop Machine Learning
• Search and Optimization: Heuristic Search

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Assessing HHL algorithm suitability for practical problems
• Classifying problems as suitable for HHL using ML
• Training data design critical for accurate classification

Innovation

• Machine Learning classifies HHL-suitable problems
• Multi-Layer Perceptrons enable accurate matrix classification
• Training data design critical for problem classification