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

We present a 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 neighbour 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 behaviour of the CCN quantum gate as a function of the ratio of the second neighbour interaction coupling constant to the first neighbour interaction coupling constant (J'/J). We found that for J'/J > = 0.02 we can have a well-defined CCN quantum gate.