The transition toward net-zero-emission power grids has become increasingly challenging due to the growing penetration of renewable energy, the integration of energy storage, and the implementation of carbon-control policies. These developments increase the operational complexity of modern power systems and require optimization approaches capable of managing multiple technical and environmental constraints. Objective: This study aims to evaluate and compare the roles of classical optimization and quantum-inspired optimization in supporting the operation of low-carbon power grids under different energy-transition scenarios. Method: This research employed a quantitative approach using scenario-based modeling and simulation. The power-grid model integrated renewable energy sources, battery energy storage, and carbon-control mechanisms. Several transition scenarios were evaluated by varying renewable-energy targets, carbon prices, and emission caps. Comparative analysis was conducted using classical optimization based on Mixed-Integer Linear Programming (MILP) as the global optimum benchmark and quantum-inspired optimization based on simulated annealing as an alternative solution approach. Findings: The results show that classical optimization produces better solution quality and higher computational efficiency than the quantum-inspired approach. However, the quantum-inspired method is still able to generate feasible and stable solutions, particularly under scenarios with high renewable-energy penetration and strict emission constraints. Implications: These findings suggest that quantum-inspired optimization has practical potential as a complementary tool for supporting low-carbon power-grid operation and energy-transition planning, especially in increasingly complex systems. Originality: The novelty of this study lies in the direct comparison between classical and quantum-inspired optimization within a unified low-carbon power-grid simulation framework. The study provides added value by positioning quantum-inspired optimization as a complement, rather than a substitute, to classical optimization in net-zero-emission power-grid transition.