CO₂ plume geothermal systems offer a promising pathway for simultaneous carbon sequestration and renewable energy production, yet their optimization remains computationally prohibitive due to the complexity of coupled multi-phase flow, heat transport, and thermodynamic processes. This study presents a novel framework that integrates Non-isothermal Unsaturated-saturated Flow and Transport modeling with quantum neural network and hybrid quantum-classical ensemble regressors to accelerate CO₂ plume geothermal system design optimization. The methodology employs latin hypercube sampling to generate 1,000 Non-isothermal Unsaturated-saturated Flow and Transport simulations across several parameter spaces, extracting statistical features that undergo rigorous selection through Boruta, Chi-squared, and Pearson correlation algorithms with a standardized weight threshold of higher than 0.75. Two quantum architectures were developed to predict six geothermal variables, including system lifetime, injected, extracted, stored CO₂ mass, cumulative energy recovery and average heat extraction rate within lifetime. The quantum models achieved exceptional accuracy for most variables in the test section, with hybrid quantum-classical ensemble regressors architectures consistently outperforming quantum neural network variants, particularly when combined with boruta feature selection. Two optimization algorithms were employed for CO₂ plume geothermal system design, including moth flame optimization for single objectives and non-dominated sorting genetic algorithm Ⅱ for multi-objective scenarios to find robust optimal solutions based on developed surrogate models for injection overpressure, well spacing near and maximizing thermal energy extraction. The framework transformed a computationally intractable optimization requiring extensive simulation time into a rapid calculation while maintaining prediction accuracy comparable to full-physics models.