Implementing a conditional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>z</mml:mi></mml:math>gate by a combination of resonant interaction and quantum interference

Abstract

We first propose an experimental scheme to implement a two-qubit conditional $z$ gate with atoms trapped in a high-$Q$ optical cavity. The scheme is based on a combination of resonant interaction and quantum interference. Further, we show that the scheme can be directly generalized to implement an $N$-qubit conditional $z$ gate, and the interaction time required to implement scheme does not change with increasing the number of qubits. This might lead to more efficient construction of quantum circuits and quantum algorithms.