Quantum Computing Algorithms for Optimization Problems: A Study Based on QAOA and MAX-CUT Simulation

Ndiana Okon Asuquo (Senior Lecturer Department of computer science. Ibom Metropolitan Polytechnic)
Siti Mariam (Universiti Teknologi Brunei (UTB))

Journal of Tecnologia Quantica
Vol. 3 No. 2 (2026)

Quantum computing represents a transformative computational paradigm capable of solving certainoptimization problems more efficiently than classical algorithms. Many real?world applicationsincluding logistics planning, transportation routing, network optimization, and machine learninginvolve combinatorial problems whose computational complexity grows exponentially with input size.This research investigates quantum algorithms for solving optimization problems, with emphasis onthe Quantum Approximate Optimization Algorithm (QAOA), Grover search techniques, andHamiltonian?based optimization frameworks. Mathematical formulations are developed for representingclassical optimization problems using quantum Hamiltonians, enabling their implementation inparameterized quantum circuits. Simulation experiments based on the MAX?CUT problem are conducted toevaluate algorithm performance. Benchmark comparisons between classical and quantum optimizationapproaches demonstrate improved scalability for quantum algorithms in simulated environments. Theresults suggest that hybrid quantum?classical optimization methods may offer practical advantagesfor solving medium?scale combinatorial problems on near?term quantum hardware. Keywords: Quantum Computing; QAOA; Combinatorial Optimization; MAX?CUT; Quantum Algorithms; Quantum Annealing