Enhancing Quantum Approximate Optimization Algorithm Through Manifold Optimization

We propose the models of Riemannian manifold optimization techniques to enhance the performance of the quantum approximate optimization algorithm (QAOA) for combinatorial optimization problems on near‐term quantum devices. The approach leverages the intrinsic geometric structure of the problem domain, addressing the nonconvexity of the QAOA objective function and overcoming challenges posed by traditional gradient descent optimizers. We introduce three Riemannian optimization methods, including Riemannian steepest descent, Riemannian conjugate gradient, and Riemannian trust regions for QAOA, and demonstrate their superiority over other techniques, such as Bayesian optimization, particle swarms, Nelder–Mead, and Adam. Riemannian trust regions generally achieve a convergence speed that is three times faster than other methods such as Adan, TuRBO, and Adam.