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We propose the implementation of a geometric-phase gate onmagnetic-field-insensitive qubits with $\hat{\sigma}^z$-dependent forces fortrapped ion quantum computing. The force is exerted by two laser beams in aRaman configuration. Qubit-state dependency is achieved by a small frequencydetuning from the virtually-excited state. Ion species with excited states oflong radiative lifetimes are used to reduce the chance of a spontaneous photonemission to less than 10$^{-8}$ per gate-run. This eliminates the main sourceof gate infidelity of previous implementations. With this scheme it seemspossible to reach the fault tolerant threshold.

High-fidelity ion-trap quantum computing with hyperfine clock states