Summary: We propose a scenario to realize quantum computers utilizing heteronuclear diatomic rovibrational states as qubits. We focused on rovibrational qubits created by simple transform limited infrared laser pulse instead of using chirped pulse. Numerical calculations show that single qubit gate operation in the electronic ground state of LiH molecule can be obtained. We also discuss the effect of temperature on the initially rotational states, and a suitable experiment condition is indicated.