The classical homotopy optimization approach has the potential to deal with highly nonlinear landscape, such as the energy landscape of QAOA problems. Following this motivation, we introduce Hamiltonian-Oriented Homotopy QAOA (HOHo-QAOA), that is 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 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.
@article{arxiv.2301.13170,
title = {Hamiltonian-Oriented Homotopy QAOA},
author = {Akash Kundu and Ludmila Botelho and Adam Glos},
journal= {arXiv preprint arXiv:2301.13170},
year = {2023}
}