  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.
