Numerical simulation of a Controlled-Controlled-Not (CCN) quantum gate in a chain of three interacting nuclear spins system

Abstract

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 ($J^{\prime }/J$). We found that for $J^{\prime }/J\ge 0.02$ we can have a well defined CCN quantum gate.

9 pages, 5 fugures

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