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

We propose the implementation of a geometric-phase gate on magnetic-field-insensitive qubits with ${\widehat{\sigma }}^z$-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.