  We propose the implementation of a geometric-phase gate on
magnetic-field-insensitive qubits with $\hat{\sigma}^z$-dependent forces for
trapped ion quantum computing. The force is exerted by two laser beams in a
Raman configuration. Qubit-state dependency is achieved by a small frequency
detuning from the virtually-excited state. Ion species with excited states of
long radiative lifetimes are used to reduce the chance of a spontaneous photon
emission to less than 10$^{-8}$ per gate-run. This eliminates the main source
of gate infidelity of previous implementations. With this scheme it seems
possible to reach the fault tolerant threshold.
