Chain of nuclear spins system quantum computer taking into account second neighbor Ising spins interaction and numerical simulation of Shor factorization of N=4

摘要

For a one-dimensional chain of four nuclear spins (1/2) and taking intoaccount first and second neighbor interactions among the spin system, we makethe numerical simulation of Shor prime factorization algorithm of the integernumber N=4 to study the influence of the second neighbor interaction on theperformance of this algorithm. It is shown that the optimum Rabi's frequency tocontrol the non-resonant effects is dominated by the second neighborinteraction coupling parameter ($J'$), and that a good Shor quantumfactorization is achieved for a ratio of second to first coupling constant of$J'/J\ge 0.04$.