We propose the implementation of a geometric-phase gate on magnetic-field-insensitive qubits with σ^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.
@article{arxiv.0707.3916,
title = {High-fidelity ion-trap quantum computing with hyperfine clock states},
author = {L. Aolita and K. Kim and J. Benhelm and C. F. Roos and H. Häffner},
journal= {arXiv preprint arXiv:0707.3916},
year = {2009}
}