The AR-AA such as AR-ADAPT-VQE and AR-AES-VQE, which cursorily assembles operators, is essentially an approximation to the original AA which subtly assembles the operators one by one. In conventional sense, an approximation usually utilizes the speedaccuracy trade-off rule. However, as the first row of Fig. shows, the accuracy provided by the AR-AAs fluctuates only within a small and acceptable range, and in some cases even it is enhanced. For instance, H 6 , at bond length R(H-H)=2.0 A, the accuracy of AR-ADAPT(3) (solid yellow line) has been improved a lot compared to that of ADAPT(3) (dashed yellow line). By Comparing the results shown in the first and second rows of Fig. together, we found that in case that the AR-AAs require more operators to construct final Ansätze than their original counterparts, they can nearly always produce more accurate results as compensation, and vice versa, attributed to the ability of AR strategy since it can generate the quasi-optimal operator order. Once the additional operators are taken into by the AR-AAs, they will be reordered properly and bring about additional energy drop. It can be concluded that the final Ansätzes generated by both AR-AAs and AAs are comparable. failure is attributed to the fact that the AR method generates too much extra iterations in order to optimize the operator sequence. That probably means the order produced by energy sorting is not a good initial guess. This factor is more fatal for small molecules like LiH which requires fewer operators. For larger molecules, extra iterations introduced by the AR method have little effect compared to the large number of N T , so the AR method can generally reduce the value of N T in AR-AES-VQE. Although (AR-)AES-VQE is more time-consuming than (AR-)ADAPT-VQE, it can generate comparable or even better results in some cases, especially in weakly correlated systems. For example, in Fig ) the region of R(Be-H)=0.8 ∼ 2.0 A, (AR-)AES-VQE(5) (blue lines) generates more accurate results than (AR-)ADAPT(3) (yellow lines) with fewer parameters, suggesting that energy sorting is more direct and effective than the gradient sorting in weakly correlated systems.