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

Gustavo V. Lopez·Lorena Lara
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Abstract

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

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Gustavo V. Lopez, Lorena Lara. 2006-08-28. Chain of nuclear spins system quantum computer taking into account second neighbor Ising spins interaction and numerical simulation of Shor factorization of N=4. https://arxiv.org/abs/quant-ph/0608148

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