Hamiltonian-Oriented Homotopy QAOA

Abstract

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.

Plant biodiversity data set of eleven mountains, China

“…Nonetheless, fixing the ansatz's structure imposes a significant restriction on exploring the cost function landscape and can prevent us from reaching the true solution. Sophisticated methods [10,22,56,59,86] have been introduced to enhance the performance of VQAs. Meanwhile, to avoid these limitations, recent attention has been directed towards automating the construction of ansatz [6,59,151,151,172], known as Quantum Architecture Search (QAS).…”