Physical implementation. of quantum gates acting on qubits does not achieve a perfect fidelity of 1. The actual output qubit may not match the targeted output of the desired gate. According to theoretical estimates, intrinsic gate fidelities >99.99% are necessary so that error correction codes can be used to achieve perfect fidelity. Here we test what fidelity can be accomplished for a CNOT gate executed by a shaped ultrafast laser pulse interacting with vibrational states of the molecule SCCl2. This molecule has been used as a test system for low-fidelity calculations before. To make out test more stringent, we include vibrational levels that do not encode the desired qubits but are dose enough in energy to interfere with population transfer by the laser pulse We use two complementary approaches optimal control theory determines what the best possible pulse can do a more constrained physical model calculates what an experiment likely can do. Optimal control theory finds pulses with fidelity >0.9999, in excess of the quantunverror correction threshold with 8 x 10(4) iterations. On the other hand, the physical model achieves only 0.9992 after 8 x 10(4) iterations. Both calculations converge as an inverse power law toward unit fidelity after >10(2) iteiations/generations. In prini:ipleithe fidelities necessary for quantum error Correction are reachable with qubits, encoded by molecular vibrations. In practice, it will be, challenging with current laboratory instrumentation because of slow convergence.Pat fidelities of 099.