A quantum approximate optimization algorithm for solving Hamilton path problem

In recent years, combinatorial optimization has been widely studied. The existing optimization solutions are prone to fall into local optimal solutions and have a lower probability of obtaining global optimal solutions. Quantum approximate optimization algorithm (QAOA) is an effective algorithm that can obtain the optimal solution with high probability. In this paper, the problem Hamiltonian is obtained by summing the problem function and the deformed constraints. Through theoretical formula derivation, the problem Hamiltonian is transformed into the Ising model. The performance of the experimental result under different optimizers and asynchronous lengths is verified on pyQPanda. The experimental results show that when using the problem Hamiltonian method set in this paper, the probability of obtaining the optimal solution is 99.59%. Compared with other methods, the proposed method can alleviate the risk of falling into local optimal solutions and obtain the global optimal solution with a higher probability.