We propose a scheme for scalable and universal quantum computation using diatomic bits with conditional dipole-dipole interaction, which are trapped within optical lattices. The qubit states are encoded as the scattering state and the bound heteronuclear molecular state of two atoms per site. The conditional dipole-dipole interaction appears between neighboring bits when they both occupy the molecular state. The realization of a universal set of quantum logic gates, which is composed of single-bit operations and a two-bit controlled-NOT gate, is presented. The readout method is also discussed
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