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Non-Local Quantum Gates: a Cavity-Quantum-Electro-Dynamics implementation

The problems related to the management of large quantum registers could be handled in the context of distributed quantum computation: unitary non-local transformations among spatially separated local processors are realized performing local unitary transformations and exchanging classical communication. In this paper, we propose a scheme for the implementation of universal non-local quantum gates such as a controlled-$\gate{NOT}$ ($\cnot$) and a controlled-quantum phase gate ($\gate{CQPG}$). The system we have chosen for their physical implementation is a Cavity-Quantum-Electro-Dynamics (CQED) system formed by two spatially separated microwave cavities and two trapped Rydberg atoms. We describe the procedures to follow for the realization of each step necessary to perform a specific non-local operation.