Quantum Harmonic Neural Networks: Application and Determination within the Context of Physics-Informed Neural Networks and Comparative Anomaly Detection

Abstract

At the juncture of quantum-defined systems and classical digital structures, cybersecurity and computing are at an inflection point where both domains converge. This thesis examined the intersection of quantum information science and artificial intelligence, focusing on quantum harmonic analysis and physics-informed neural networks (PINNs). The research approach evaluated data and system behavior from a scientific, experimental perspective. Comparative studies were conducted to assess the proposed hypothesis. Specifically, the research question explored machine learning architecture and artificial intelligence design components in which PINN integration was engineered to support high mathematical precision and anomaly detection within a cybersecurity setting. The study involved coded experimentation using designated AI structures enhanced with simulated quantum processing, producing quantitative output for analysis and scientific interpretation. Methodologies were employed to formalize experimentation with a Geometrically Coherent Quantum Harmonic Neural Network (GCQHNN) and an enhanced physics-informed neural network. The experiment evaluated statistical variability and compared the proposed networks with classical machine learning models and related algorithms when challenged by known and unknown cyberattack vectors.