  The method of iterated resolvents is used to obtain an effective Hamiltonian
for neighbouring qubits in the Kane solid state quantum computer. In contrast
to the adiabatic gate processes inherent in the Kane proposal we show that free
evolution of the qubit-qubit system, as generated by this effective
Hamiltonian, combined with single qubit operations, is sufficient to produce a
controlled-NOT (c-NOT) gate. Thus the usual set of universal gates can be
obtained on the Kane quantum computer without the need for adiabatic switching
of the controllable parameters as prescribed by Kane. Both the fidelity and
gate time of this non-adiabatic c-NOT gate are determined by numerical
simulation.
