Application of Quantum Approximate Optimization Algorithm in Three- Dimensional Matching Problem

The three-dimensional matching problem is a classic NP-complete problem in combinatorial optimization, with wide applications in resource allocation, task scheduling, and many other practical scenarios. Traditional algorithms for solving the three-dimensional matching problem face the challenge of high time complexity, making it difficult to solve large-scale problems within a reasonable time frame. To improve the solution efficiency, a quantum circuit solution based on the Quantum Approximate Optimization Algorithm (QAOA) is proposed. By constructing a mathematical model of the three-dimensional matching problem, the corresponding Hamiltonian expression is derived. A QAOA-based quantum circuit is designed and the parameters of the parameterized quantum gates are optimized using the classical optimization algorithm COBYLA. Simulation experiments are performed using IBM's quantum development framework Qiskit. The experimental results show that the solution to the three-dimensional matching problem can be obtained with 84% probability in polynomial time, verifying the feasibility and effectiveness of solving the three-dimensional matching problem based on the Quantum Approximate Optimization Algorithm.