Quantum-Inspired Fast Algorithm and Circuit Realization for Constrained Combinatorial Optimization Problem.

Constrained combinatorial optimization (CCO) problems are prevalent across various fields and represent key challenges in computational science and engineering. Although numerous classical and quantum algorithms have been proposed to tackle these problems, substantial limitations still persist. Classical algorithms exhibit exponential computational complexity growth with scale and persistent vulnerability to local minima traps. Quantum computing, while offering theoretical advantages through global superposition, faces practical barriers such as short decoherence times and current hardware limitations. To address these challenges, we propose a quantum-inspired fast algorithm for solving CCO problems. Our approach enhances global search capability with superposition encoding and avoids constraint-induced local minima​​ via a project-feedback strategy. Particularly, our method aligns with mature electronics manufacturing and demonstrates a proof-of-concept implementation in classical systems, indicating high-efficiency potential for solving constrained optimization problems.