A spin cluster of 3 spin 1/2 particles has been studied as a qubit system. A time dependent magnetic field is applied to control the time evolution of the cluster. The lowest energy level of the cluster has the total spin 1/2 separated far away from the excited states and can be used as a qubit register. The universal 1-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the 6 basic 1-qubit gates can be realized by adjusting the applied time dependent magnetic field. As a many-body system, this qubit system is expected to be robust against the dissipation effect of the thermal radiation fields from the environment.