  An approach to the construction of the CNOT quantum logic gate for a
4-dimensional coupled-qubit model with weak but otherwise arbitrary coupling
has been given recently [M. R. Geller et al., Phys. Rev. A, 012320 (2010)]. How
does the resulting fidelity depend on the form of qubit-qubit coupling? In this
paper we calculate intrinsic fidelity curves (fidelity in the absence of
decoherence versus total gate time) for a variety of qubit-qubit interactions,
including the commonly occurring isotropic Heisenberg and XY models, as well as
randomly generated ones. For interactions not too close to that of the Ising
model, we find that the fidelity curves do not significantly depend on the form
of the interaction, and we calculate the resulting interaction-averaged
fidelity curve for the non-Ising-like cases and a criterion for determining its
applicability.
