<![CDATA[High-fidelity two-qubit gates are essential for scalable quantum computation in superconducting transmon circuits. However, weak anharmonicity can induce leakage outside the computational subspace, while relaxation and dephasing reduce gate fidelity. This study presents a numerical simulation of a CNOT gate in a coupled two-transmon system. Each transmon is modeled as a three-level system, where |0⟩ and |1⟩ form the computational subspace, while |2⟩ is included to evaluate leakage. The control pulses are optimized using a two-channel chopped random basis (CRAB) method. The pulse u_1 (t) is applied to the control transmon as the main drive, while u_2 (t) is applied to the target transmon as a correction drive. The system is simulated under closed- and open-system conditions. In the open system, energy relaxation and pure dephasing are included through the Lindblad master equation. CRAB optimization improves the CNOT basis fidelity from 0.65 to 0.96 in the closed system and from 0.65 to 0.95 in the open system. The final leakage remains small, around 10^(-3). These results indicate that the correction drive can improve CNOT gate performance while keeping leakage low.]]>
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