A Hybrid Quantum–Classical Machine Learning Framework for Black Carbon Forecasting

Abstract Black carbon (BC) is a critical short-lived climate pollutant with severe health and climate impacts, yet forecasting its hourly dynamics remains challenging due to nonlinear interactions between meteorological conditions and co-emitted pollutants. Accurate forecasting is particularly relevant in regions facing persistent air quality issues, where BC frequently exceeds recommended limits and poses significant risks to public health. This study develops a data-driven forecasting framework that integrates ensemble learning with hybrid quantum–classical neural architectures, benchmarked using 8760 hourly records from Santa Catarina in the Monterrey Metropolitan Area (Mexico). Ensemble methods provided the most reliable baseline, with XGBoost ( $\mathrm{R}^{2} = 0.80$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.80</mml:mn> </mml:math> , RMSE = 614.32 ng m −3 ) and CatBoost ( $\mathrm{R}^{2} = 0.80$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.80</mml:mn> </mml:math> , RMSE = 614.06 ng m −3 ) effectively capturing pollutant–meteorology dependencies. In contrast, a purely quantum neural network underperformed ( $\mathrm{R}^{2} = 0.62$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.62</mml:mn> </mml:math> ), whereas its hybrid quantum–classical counterpart improved predictive accuracy ( $\mathrm{R}^{2} = 0.72$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.72</mml:mn> </mml:math> ) and exhibited more stable convergence, highlighting the benefits of combining quantum representations with classical optimization under current hardware constraints. Dimensionality reduction through Principal Component Analysis (six components retaining 91% of variance) had a limited effect on ensemble models but reduced the ability of neural and quantum architectures to capture extreme pollution events above 3000 ng m −3 . These findings elucidate how machine learning architectures represent the temporal dynamics of short-lived climate pollutants and support the development of adaptive early-warning systems for air quality management. The proposed hybrid framework provides a reproducible and extensible basis for applying quantum computing techniques to environmental forecasting, establishing a methodological foundation for future quantum–environmental research.