We comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial optimization problems. Our survey includes over 100 different mixing unitaries, and we combine each mixer with both the standard phase separator unitary representing the objective function and a thresholded version. Our numerical tests for randomly chosen instances of the unconstrained optimization problems Max 2-SAT and Max 3-SAT reveal that the traditional transverse-field mixer with the standard phase separator performs best for problem sizes of 8 through 14 variables, while the recently introduced Grover mixer with thresholding wins at problems of size 6. This result (i) corrects earlier work suggesting that the Grover mixer is a superior mixer based only on results from problems of size 6, thus illustrating the need to push numerical simulation to larger problem sizes to more accurately predict performance; and (ii) it suggests that more complicated mixers and phase separators may not improve QAOA performance.

翻译：我们通过大规模数值模拟，系统比较了多种量子交替算子Ansatz（QAOA）实现方案在无约束组合优化问题中寻找近似解与最优解的性能表现。本研究涵盖了超过100种不同的混合幺正算符，并将每种混合算子分别与标准相位分离器（代表目标函数）及其阈值化版本相结合。针对随机生成的无约束优化问题实例（Max 2-SAT与Max 3-SAT）的数值测试表明：对于8至14个变量的规模，采用标准相位分离器的传统横场混合算子表现最优；而在6变量问题上，最近提出的阈值化Grover混合算子更具优势。这一发现：（i）修正了此前仅基于6变量问题结果就断言Grover混合算子更优的结论，凸显了将数值模拟扩展至更大规模以准确预测性能的必要性；（ii）暗示更复杂的混合算子与相位分离器可能无法提升QAOA的性能表现。