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We present the study of a quantum Controlled-Controlled-Not gate, implementedin a chain of three nuclear spins weakly Ising interacting between all of them,that is, taking into account first and second neighbor spin interactions. Thisimplementation is done using a single resonant $\pi$-pulse on the initial stateof the system (digital and superposition). The fidelity parameter is used todetermine the behavior of the CCN quantum gate as a function of the ratio ofthe second neighbor interaction coupling constant to the first neighborinteraction coupling constant ($J'/J$). We found that for $J'/J\ge 0.02$ we canhave a well defined CCN quantum gate.Comment: 9 pages, 5 fugure

Numerical simulation of a controlled–controlled-not (CCN) quantum gate in a chain of three interacting nuclear spins system