A scheme is proposed for achieving a controlled phase gate using interaction between atomic spin dipoles. Further, the spin states are prepared in coherent population trap states (CPTs), which are robust against perturbations, laser fluctuations etc. We show that one-qubit and two-qubit operations can easily be obtained in this scheme. The scheme is also robust against decoherences due to spontaneous emissions as the CPT states used are dressed states formed out of Zeeman sublevels of ground states of the bare atom. However, certain practical issues are of concern in actually obtaining the scheme, which are also discussed at the end of this paper.