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The Quantum Approximate Optimization Algorithm (QAOA) is a prospective hybrid quantum-classical algorithm, which is widely used to solve combinatorial optimization problems. One major challenge of QAOA lies in finding optimal parameters of the parameterized quantum circuit. To meet this challenge, some scholars put forward heuristic parameter initialization strategies. Interpolation-based strategy (INTERP) is a heuristic parameter initialization strategy in QAOA for Maxcut. Compared with random initialization, INTERP greatly reduces the time to find quasi-optimal solutions. In this paper, we first propose INTERP+ to save the running costs. Compared with INTERP, INTERP+ takes advantage of multi-interpolation and cuts down at least half the number of rounds of optimization. The simulation results demonstrate that INTERP+ saves about 2/3 of running time when it can obtain the same quasi-optimal solutions as INTERP. In addition, we present Multi-INTERP+ by introducing multi-start and selection. The simulation results show that Multi-INTERP+ can not only get the same quasi-optimal solutions as INTERP but also get higher average performance than INTERP and INTERP+.

A new vector theory which concerns the necessary and sufficient conditions of the self-trapping of a linearly polarized light beam in Kerr media is presented after a generalization of Fermat's principle. It is rigidly proven under these conditions that 1+1-dimensional spatial solitons can exist in Kerr media but 2+1-dimensional solitons cannot. A new form of the general equation for 1+1-dimensional solitons in Kerr media is put forward and some of its solutions have been obtained.