  Four-level systems in quantum optics, and for representing two qubits in
quantum computing, are difficult to solve for general time-dependent
Hamiltonians. A systematic procedure is presented which combines analytical
handling of the algebraic operator aspects with simple solutions of classical,
first-order differential equations. In particular, by exploiting $su(2) \oplus
su(2)$ and $su(2) \oplus su(2) \oplus u(1)$ sub-algebras of the full SU(4)
dynamical group of the system, the non-trivial part of the final calculation is
reduced to a single Riccati (first order, quadratically nonlinear) equation,
itself simply solved. Examples are provided of two-qubit problems from the
recent literature, including implementation of two-qubit gates with Josephson
junctions.
