Multilevel leapfrogging initialization for quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is a prospective hybrid quantum-classical algorithm widely used to solve combinatorial optimization problems. However, the external parameter optimization required in QAOA tends to consume extensive resources to find the optimal parameters of the parameterized quantum circuit, which may be the bottleneck of QAOA. To meet this challenge, we first propose multilevel leapfrogging learning (M-Leap) that can be extended to quantum reinforcement learning, quantum circuit design, and other domains. M-Leap incrementally increases the circuit depth during optimization and predicts the initial parameters at level $p+r$ ($r>1$) based on the optimized parameters at level $p$, cutting down the optimization rounds. Then, we propose a multilevel leapfrogging-interpolation strategy (MLI) for initializing optimizations by combining M-Leap with the interpolation technique. We benchmark its performance on the Maxcut problem. Compared with the Interpolation-based strategy (INTERP), MLI cuts down at least half the number of rounds of optimization for the classical outer learning loop. Remarkably, the simulation results demonstrate that the running time of MLI is 1/3 of INTERP when MLI gets quasi-optimal solutions. In addition, we present the greedy-MLI strategy by introducing multi-start, which is an extension of MLI. The simulation results show that greedy-MLI can get a higher average performance than the remaining two methods. With their efficiency to find the quasi-optima in a fraction of costs, our methods may shed light in other quantum algorithms