Numerical determination of nuclear magnetic resonance frequency of the single-qubit operation in kane´s quantum computer

In this study, the second-order perturbation theory is used to determine the nuclear magnetic resonance frequency of a donor ³¹P doped inside a silicon substrate under the influence of an applied electric field. This phosphorus donor has been suggested for operation as a qubit for the realization of a solid-state scalable quantum computer. The operation of the qubit is achieved by a combination of the rotation of the phosphorus nuclear spin through a globally applied magnetic field and the selection of the phosphorus nucleus through a locally applied electric field. To realize the selection function, it is required to know the relationship between the applied electric field and the change of the nuclear magnetic resonance frequency of phosphorus.