Abstract
We propose a scheme for realizing a two-qubit quantum phase gate between atoms inside a high-$Q$ optical cavity. In the scheme, the dispersive interaction between atoms and the cavity field induces photon-number Stark shift, which can yield a resonant interaction inside one selected atom-field subspace and leave the others in a highly dispersive regime. Due to the selective atom-cavity interaction, (1) the scheme only requires commonly addressing the atoms inside the optical cavity during the gate operation, and (2) it can be directly used to implement an $N$-qubit conditional phase gate. These properties can significantly reduce the number of operations for implementing quantum computation and quantum algorithms.
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