The paper presents evidence for a scaling advantage in approximate optimization using quantum annealing, relative to the best classical heuristic algorithm, parallel tempering with isoenergetic cluster moves (PT-ICM). The study focuses on a family of 2D spin-glass problems with high-precision spin-spin interactions. Quantum annealing correction (QAC) is implemented to enhance the success probability and mitigate control errors, resulting in over 1,300 error-suppressed logical qubits on a degree-5 interaction graph. The time-to-epsilon metric is used to benchmark the performance, and the results show that quantum annealing exhibits a scaling advantage over PT-ICM at sampling low-energy states with an optimality gap of at least 1.0%. This is the first demonstration of an algorithmic quantum speedup in approximate optimization. The study highlights the importance of quantum error suppression techniques and the potential for quantum annealing to achieve near-linear scaling at smaller optimality gaps compared to classical methods.The paper presents evidence for a scaling advantage in approximate optimization using quantum annealing, relative to the best classical heuristic algorithm, parallel tempering with isoenergetic cluster moves (PT-ICM). The study focuses on a family of 2D spin-glass problems with high-precision spin-spin interactions. Quantum annealing correction (QAC) is implemented to enhance the success probability and mitigate control errors, resulting in over 1,300 error-suppressed logical qubits on a degree-5 interaction graph. The time-to-epsilon metric is used to benchmark the performance, and the results show that quantum annealing exhibits a scaling advantage over PT-ICM at sampling low-energy states with an optimality gap of at least 1.0%. This is the first demonstration of an algorithmic quantum speedup in approximate optimization. The study highlights the importance of quantum error suppression techniques and the potential for quantum annealing to achieve near-linear scaling at smaller optimality gaps compared to classical methods.