We have found that encapsulated atoms in fullerene molecules, which carry a spin, can be used for fast quantum computing. We describe the scheme for performing quantum computations, going through the preparation of the qubit state and the realization of a two-qubit quantum gate. When we apply a static magnetic field to each encased spin, we find out the ideal design for the preparation of the quantum state. Therefore, adding to our system a time dependent magnetic field, we can perform a phase-gate. The operational time related to a π-phase gate is of the order of ns. This finding shows that, during the decoherence time, which is proportional to micrometer/s, we can perform many thousands of gate operations. In addition, the two-qubit state which arises after a π-gate is characterized by a high degree of entanglement. This opens a new avenue for the implementation of fast quantum computation.