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.
Quantum theory, NMR, NQR, Spin Nuclear, SU(n), Pauli Matrices, Gell Mann matrices, Qubit, Qutrit and qudit