Hamiltonian-oriented homotopy quantum approximate optimization algorithm

The classical homotopy optimization approach has the potential to deal with highly nonlinear landscapes, such as the energy landscape of quantum approximate optimization algorithm (QAOA) problems. Following this motivation, we introduce Hamiltonian-oriented homotopy QAOA (HOHo-QAOA), a heuristic method for combinatorial optimization using QAOA, based on classical homotopy optimization. The method consists of a homotopy map that produces an optimization problem for each value of the interpolating parameter. Therefore, HOHo-QAOA decomposes the optimization of QAOA into several loops, each using a mixture of the mixer and the objective Hamiltonian for cost function evaluation. Furthermore, we conclude that the HOHo-QAOA improves the search for low-energy states in the nonlinear energy landscape and outperforms other variants of QAOA.