Cavity QED implementation of the multi-qubit refined Deutsch-Jozsa algorithm

We theoretically study the realization of a multi-qubit refined Deutsch-Jozsa (DJ) algorithm using resonant interaction of many Rydberg atoms with a single-mode microwave cavity, in which the multi-qubit controlled phase gates could be accomplished efficiently. We show how to achieve a multi-qubit refined DJ algorithm in high fidelity, even in the case of a weak cavity decay and some imperfection. We argue that the required operations in our scheme are almost within the present experimental possibilities.