  Creation of quantum computer is outstanding fundamental and practical
problem. The quantum computer could be used for execution of very complicated
tasks which are not solvable with the classical computers. The first prototype
of solid state quantum computer was created in 2009 with superconducting
qubits. However, it suffers from the decoherent processes and it is desirable
to find more practical encoding of qubits with long-lived coherence. It could
be single impurity or vacancy centers in solids, but their interaction with
electromagnetic radiation is rather weak. So, here, ensembles of atoms were
proposed for the qubit encoding by using the dipole blockade mechanism in order
to turn multilevel systems in two level ones. But dipole-dipole based blockade
introduces an additional decoherence that limits its practical significance.
Recently, the collective blockade mechanism has been proposed for the system of
three-level atoms by using the different frequency shifts for the Raman
transitions between the collective atomic states characterized by a different
number of the excited atoms. Here, we propose two qubit gate by using another
collective blockade mechanism in the system of two level atoms based on
exchange interaction via the virtual photons between the multi-atomic ensembles
in the resonator. Also we demonstrate the possibility of three qubit gate
(Controlled SWAP gate) using a suppression of the swap-process between two
multi-atomic ensembles due to dynamical shift of the atomic levels controlled
by the states of photon encoded qubit.
