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Creation of quantum computer is outstanding fundamental and practicalproblem. The quantum computer could be used for execution of very complicatedtasks which are not solvable with the classical computers. The first prototypeof solid state quantum computer was created in 2009 with superconductingqubits. However, it suffers from the decoherent processes and it is desirableto find more practical encoding of qubits with long-lived coherence. It couldbe single impurity or vacancy centers in solids, but their interaction withelectromagnetic radiation is rather weak. So, here, ensembles of atoms wereproposed for the qubit encoding by using the dipole blockade mechanism in orderto turn multilevel systems in two level ones. But dipole-dipole based blockadeintroduces an additional decoherence that limits its practical significance.Recently, the collective blockade mechanism has been proposed for the system ofthree-level atoms by using the different frequency shifts for the Ramantransitions between the collective atomic states characterized by a differentnumber of the excited atoms. Here, we propose two qubit gate by using anothercollective blockade mechanism in the system of two level atoms based onexchange interaction via the virtual photons between the multi-atomic ensemblesin the resonator. Also we demonstrate the possibility of three qubit gate(Controlled SWAP gate) using a suppression of the swap-process between twomulti-atomic ensembles due to dynamical shift of the atomic levels controlledby the states of photon encoded qubit.

Fast and robust two- and three-qubit swapping gates on multi-atomic ensembles in quantum electrodynamic cavity