Solving Maximum Cut Problem with Multi-objective Enhance Quantum Approximate Optimization Algorithm

This article presents a novel approach to enhancing the performance of the Quantum Approximate Optimization Algorithm (QAOA), a method used to tackle combinatorial optimization problems. However, it has many disadvantages because of classical optimizers for optimizing only the expectation. Our approach employs multi-objective programming techniques to simultaneously improve both the expectation value and the probability of the optimal solution within the QAOA framework. We apply the NSGA II (Non-dominated Sorting Genetic Algorithm II) to solve this problem. To evaluate the effectiveness of our approach, we conduct experiments using the maximum cut problem with weighted edge graphs, demonstrating its efficiency.