Manipulating two-spin coherences and qubit pairs

A compact derivation is given for propagators of a wide class of time-dependent Hamiltonians that describe coupled spin (qubit) pairs. As many as eight of the 16 operators in the system, each with its own time-dependent coefficient, can be handled with no more difficulty than a single spin in a magnetic field. A single first-order (in time), quadratically nonlinear differential equation for a classical function is the only nontrivial ingredient in constructing the full quantum propagator for a wide variety of magnetic coherences and qubit interactions.