Mathematical Evaluation of Classical and Quantum Predictive Models Applied to PM2.5 Forecasting in Urban Environments

Air quality modeling has become a strategic area within data science, particularly in urban contexts where pollution exhibits high variability and nonlinear dynamics. This study provides a mathematical and computational comparison between two predictive paradigms: the classical Long Short-Term Memory (LSTM) model, designed for sequential analysis of time series, and the quantum model Quantum Support Vector Machine (QSVM), based on kernel methods applied in Hilbert spaces. Both approaches are applied to real PM2.5 concentration data collected at the Plaza Castilla monitoring station (Madrid) over the period 2017–2024. The LSTM model demonstrates moderate accuracy for smooth seasonal trends but shows limited performance in detecting extreme pollution events. In contrast, the QSVM achieves perfect binary classification through a quantum kernel based on angle encoding, with significantly lower training time and computational cost. Beyond the empirical results, this work highlights the growing potential of Quantum Artificial Intelligence as a hybrid paradigm capable of extending the boundaries of classical models in complex environmental prediction tasks. The implications point toward a promising transition to quantum-enhanced predictive systems aimed at advancing urban sustainability.