  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.
