  We present the study of a quantum Controlled-Controlled-Not gate, implemented
in a chain of three nuclear spins weakly Ising interacting between all of them,
that is, taking into account first and second neighbor spin interactions. This
implementation is done using a single resonant $\pi$-pulse on the initial state
of the system (digital and superposition). The fidelity parameter is used to
determine the behavior of the CCN quantum gate as a function of the ratio of
the second neighbor interaction coupling constant to the first neighbor
interaction coupling constant ($J'/J$). We found that for $J'/J\ge 0.02$ we can
have a well defined CCN quantum gate.
