Quantum dynamics of the cubit system in external fields

A system of two dipole-dipole interacting two-level elements (qubits) in external fields is considered. It is shown that using the coherent states (CS) of the dynamic symmetry group of the $SU(2)\times SU(2)$ system, the time evolution can be reduced to the "classical" dynamics of the complex parameters of the CS. The trajectories of the CS are constructed and the time dependences of the probability of finding qubits at the upper levels are calculated.