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We have studied a system composed by two endohedral fullerene molecules. We have found that
this system can be used as good candidate for the realization of Quantum Gates. Each of these molecules
encapsules an atom carrying a spin, therefore they interact through the spin dipole interaction. We show
that a phase gate can be realized if we apply static and time dependent magnetic fields on each encased
spin. We have evaluated the operational time of a pi-phase gate, which is of the order of ns. We made a
comparison between the theoretical estimation of the gate time and the experimental decoherence time for
each spin. The comparison shows that the spin relaxation time is much larger than the pi-gate operational
time. Therefore, this indicates that, during the decoherence time, it is possible to perform some thousands
of quantum computational operations. Moreover, through the study of concurrence, we get very good
results for the entanglement degree of the two-qubit system. This finding opens a new avenue for the
realization of Quantum Computers.