An efficient scheme is proposed to carry out gate operations on an array of
trapped Yb+ ions, based on a previous proposal using both electronic and
nuclear degrees of freedom in a magnetic field gradient. For this purpose we
consider the Paschen-Back regime (strong magnetic field) and employ a
high-field approximation in this treatment. We show the possibility to suppress
the unwanted coupling between the electron spins by appropriately swapping
states between electronic and nuclear spins. The feasibility of generating the
required high magnetic field is discussed
