An angle rounding parameter initialization technique for ma-QAOA

The multi-angle quantum approximate optimization algorithm (ma-QAOA) is a recently introduced algorithm that gives at least the same approximation ratio as the quantum approximate optimization algorithm (QAOA) and, in most cases, gives a significantly higher approximation ratio than QAOA. One drawback to ma-QAOA is that it uses significantly more classical parameters than QAOA, so the classical optimization component more complex. In this paper, we motivate a new parameter initialization strategy in which angles are initially randomly set to multiples of $\pi/8$ between $-\pi$ and $\pi$ and this vector is used to seed one round of BFGS. We find that this parameter initialization strategy gives average approximation ratios of $0.900$, $0.982$, and $0.997$ for $p = 1, 2, 3$ layers of ma-QAOA. This is comparable to the average approximation ratios of ma-QAOA where the optimal parameters are found using BFGS with 1 random starting seed, which are $0.900$, $0.982$, and $0.996$. We also test another parameter initialization strategy in which angles corresponding to maximal degree vertices in the graph are set to 0 while all other are randomly initialized to random multiples of $\pi/8$. Using this strategy, the average approximation ratios are $0.897$, $0.984$, and $0.997$.