Quantum Computing Algorithms for Optimization Problems: A Study Based on QAOA and MAX-CUT Simulation - Asuquo, Ndiana Okon; Mariam , Siti (Journal of Tecnologia Quantica, 2026)
Quantum computing represents a transformative computational paradigm capable of solving certain optimization problems more efficiently than classical algorithms. Many real?world applications including logistics planning, transportation routing, network optimization, and machine learning involve combinatorial problems whose computational complexity grows exponentially with input size. This research investigates quantum algorithms for solving optimization problems, with emphasis on the Quantum Approximate Optimization Algorithm (QAOA), Grover search techniques, and Hamiltonian?based optimization frameworks. Mathematical formulations are developed for representing classical optimization problems using quantum Hamiltonians, enabling their implementation in parameterized quantum circuits. Simulation experiments based on the MAX?CUT problem are conducted to evaluate algorithm performance. Benchmark comparisons between classical and quantum optimization approaches demonstrate improved scalability for quantum algorithms in simulated environments. The results suggest that hybrid quantum?classical optimization methods may offer practical advantages for solving medium?scale combinatorial problems on near?term quantum hardware. Keywords: Quantum Computing; QAOA; Combinatorial Optimization; MAX?CUT; Quantum Algorithms; Quantum Annealing