Quantum annealing initialization of the quantum approximate optimization algorithm

TLDR

The quantum approximate optimization algorithm (QAOA) is a promising near‑term quantum algorithm with modest circuit depth, yet its required external parameter optimization can become a performance bottleneck. The study aims to explore the QAOA optimization landscape and develop heuristic initialization methods. The authors visualize the QAOA landscape for MaxCut on random graphs, revealing that random initialization often converges to sub‑optimal local minima, and propose a Trotterized quantum annealing (TQA) protocol with a tunable time step to initialize parameters. TQA initialization avoids false minima over a wide range of time steps, matching the best performance among exponentially many random starts, with the optimal time step aligning with the onset of Trotter errors, thereby offering practical initialization strategies and highlighting links between QAOA and quantum annealing.

Abstract

The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with sub-optimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveals new connections between QAOA and quantum annealing.