The present work focused on theoretical studies in the molecular quantum computing with vibrational qubits and how the molecular vibrational properties affect the fidelity of the logic gates. By using the Optimal Control Theory to shape a femtosecond laser and numerical propagation of laser-driven vibrational wave packets, the work analyzed how the vibrational properties of a two-qubit system affect the accuracy of the quantum gates and how to effectively control the vibrational state-to-state transitions. From these studies, the anharmonicities were found to be very important for the control...