Unitary Coupled Cluster Operator

In quantum computing, we always want to deal with unitary evolution operators. That's why the traditional definition of the Coupled Cluster ansatz is modified to the so-called Unitary Coupled Cluster , in which the exponent of the cluster operator is changed to $\operatorname{e}^T \to \operatorname{e}^{T-T^\dagger}$ Generally, there are two ways of making an anti-Hermitian operator out of an arbitrary operator $T$ : $$ \begin{alignedat}{4} &1.\quad &&T \to &&(T-T^\dagger)\ &2.\quad &&T \to i&&(T+T^\dagger) \end{alignedat}