  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 on each encased spin static and time
dependent magnetic field. 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.
