One-step implementation of an N-qubit controlled-phase gate with neutral atoms trapped in an optical cavity

We present a one-step scheme for direct implementation of an N-qubit controlled-phase gate with atoms trapped in a high-Q optical cavity without resorting to a sequence of single- and two-qubit gates. The interaction time that is required to implement the scheme does not rise with increasing number of qubits. This might lead to more efficient construction of quantum circuits and quantum algorithms.