Quantum circuit model is the most popular paradigm for implementing complex quantum computation. Based on Cartan decomposition, it is shown 2(N−1)$2(N-1)$ generalized controlled‐X (GCX) gates, 6 single‐qubit rotations about the y‐ and z‐axes, and N+5$N+5$ single‐partite y‐ and z‐rotation‐types which are defined in this paper are sufficient to simulate a controlled‐unitary gate Ucu(2⊗N)$\mathcal {U}_{\text{cu}(2\otimes N)}$ with A$\text{A}$ controlling on C2⊗CN$\mathbb {C}^2\otimes \mathbb {C}^N$. In the scenario of the unitary gate Ucd(M⊗N)$\mathcal {U}_{\text{cd}(M\otimes N)}$ with M≥3$M\ge 3$ that is locally equivalent to a diagonal unitary on CM⊗CN$\mathbb {C}^M\otimes \mathbb {C}^N$, 2M(N−1)$2M(N-1)$ GCX gates and 2M(N−1)+10$2M(N-1)+10$ single‐partite y‐ and z‐rotation‐types are required to simulate it. The quantum circuit for implementing Ucu(2⊗N)$\mathcal {U}_{\text{cu}(2\otimes N)}$ and Ucd(M⊗N)$\mathcal {U}_{\text{cd}(M\otimes N)}$ are presented. Furthermore, it is found that Ucu(2⊗2)$\mathcal {U}_{\text{cu}(2\otimes 2)}$ with A$\text{A}$ controlling has Schmidt rank two, and in other cases the diagonalized form of the target unitaries can be expanded in terms of specific simple types of product unitary operators. A quantum circuit of the controlled‐unitary operation with side controlling on C2⊗CN$C^{2} \otimes C^{N}$ system is designed by utilizing Cartan decomposition technique. The synthesis is extended to the unitary operations on CM⊗CN$C^{M} \otimes C^{N}$ which are locally equivalent to diagonal unitary operations. Additionally, the possible Schmidt rank of these unitary operations is presented in detail.