Hamiltonian-Oriented Homotopy QAOA

TL;DR

HOHo-QAOA is a novel heuristic that leverages classical homotopy optimization to improve the search for low-energy states in QAOA, outperforming other variants in complex energy landscapes.

Contribution

The paper introduces HOHo-QAOA, a new homotopy-based heuristic for QAOA that enhances optimization in nonlinear energy landscapes.

Findings

HOHo-QAOA improves low-energy state search.

HOHo-QAOA outperforms other QAOA variants.

The method decomposes QAOA optimization into multiple loops.

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.