ÛT is termed as Trotterized UCCSD Ansätze. The detailed form of X is shown in Eq. S2 in the supporting information (SI). X originates from the non-commutation between different anti-hermitian operators Tp , and it is a product of infinite series of nested commutators. The specific form of X( ⃗ θ) is quite complicated and is obviously related to the order of cluster operators. Grimsley et al. made numerical simulations of the Trotterized UCCSD Ansätze with a large number of different operator orders, and observed a significant, system-dependent variation in the energies. These variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. A method proposed by Izmaylov et al. may entirely eliminate the problem caused by the operator order in UCCSD Ansätze by using Lie sub-groups. However, constructing the Ansätze by means of sub-algebra will introduce additional number of operators, resulting in a more complicated quantum circuit.