  A self-contained approach to studying the unitary evolution of coupled qubits
is introduced, capable of addressing a variety of physical systems described by
exchange Hamiltonians containing Rabi terms. The method automatically
determines both the Weyl chamber steering trajectory and the accompanying local
rotations. Particular attention is paid to the case of anisotropic exchange
with tracking controls, which is solved analytically. It is shown that, if
computational subspace is well isolated, any exchange interaction can always
generate high-fidelity, single-step controlled-NOT (CNOT) logic, provided that
both qubits can be individually manipulated. The results are then applied to
superconducting qubit architectures, for which several CNOT gate
implementations are identified. The paper concludes with consideration of two
CNOT gate designs having high efficiency and operating with no significant
leakage to higher-lying non-computational states.
