Solving Edge-Weighted Maximum Clique Problem with DCA Warm-Start Quantum Approximate Optimization Algorithm

The Quantum Approximate Optimization Algorithm is a hybrid quantum-classic algorithm used for solving combinatorial optimization. However, this algorithm performs poorly when solving the constrained combinatorial optimization problem. To deal with this issue, we consider the warm-start Quantum Approximate Optimization Algorithm for solving constrained problems. This article presents a new method for improving the performance of the Quantum Approximate Optimization Algorithm, with the Difference of Convex Optimization. Our approach focuses on the warm-start version of the algorithm and uses the Difference of Convex optimization to find the warm-start parameters. To show our method’s efficiency, we do several experiments on the edge-weighted maximum clique problem and see a good result.