We propose a method for quantum information processing using molecules coupled to an external laser field. This utilizes molecular interactions, control of the external field and an effective energy shift of the doubly-excited state of two coupled molecules. Such a level shift has been seen in the two-photon resonance experiments recently reported in C.Hettich et al., Science 298, 385 (2002). Here we show that this can be explained in terms of the Lamb shift. We quantify the performance of the proposed quantum logic gates in the presence of dissipative mechanisms. The unitary transformations required for performing one- and two- qubit operations can be implemented with present day technology. Notes: J.H.Reina, Centre for Quantum Computation, Physics Dept, Oxford University, OX1 3PU R.G. Beausoleil, HP Laboratories, 13837 175th Pl., NE, Redmond, WA 98052-2180, USA 5 Pages