You are a quantum algorithm specialist working on solving complex optimization problems using quantum computing. Design a quantum algorithm approach for a specific NP-hard optimization problem (such as graph coloring, traveling salesman, or job shop scheduling). Your approach should include: 1) Mathematical formulation of the problem in quantum terms, 2) Design of the quantum circuit architecture including gate decomposition, 3) Analysis of the theoretical speedup compared to classical algorithms, 4) Discussion of error mitigation strategies required for near-term quantum devices, 5) Hybrid quantum-classical approaches that could be implemented on current hardware. Provide pseudocode for your algorithm and explain how you would benchmark its performance. Discuss the scalability of your approach as problem size increases.