Gates for the Kane Quantum Computer in the Presence of Dephasing

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a CNOT gate is $8.3 \times 10^{-5}$. We also compute the fidelities of Z, X, Swap, and Controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.