In this article we have considered the effect of a magnetic field, the Zeeman effect, nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) on nuclei with spin S ½ looked.Then energy levels, transition frequencies and the energy spectra for the nuclear spins have specified.After using the group definition SU(2), SU(3), SU(4), SU(N) OR SU(2S+1), In quantum mechanics and quantum computation the range nuclear energy levels sin to one qubit, qutrit and qudit assign.We have defined the quantum states.
A method for performing quantum state tomography for quadrupole nuclei is presented in this paper. First, it is shown that upon appropriate phase cycling, the nuclear-magnetic-resonance (NMR) intensities of quadrupole nuclei depend only on diagonal elements of the density-matrix. Thus, a method for obtaining the density-matrix elements, which consists of dragging off-diagonal elements into the main diagonal using fine phase-controlled selective radio-frequency pulses, was derived. The use of the method is exemplified through
23Na NMR (nuclear spin
I=3∕2) in a lyotropic liquid crystal at room temperature, in three applications: (a) the tomography of pseudopure states, (b) the tomography of the quadrupole free evolution of the density matrix, and (c) the unitary state evolution of each qubit in the system over the Bloch sphere upon the application of a Hadamard gate. Further applications in the context of pure NMR and in the context of quantum information processing, as well as generalizations for higher spins, are discussed.