Controllability of spin 1 systems and realization of ternary SWAP gate in two spin 1 systems coupled with Ising interaction

In this paper,we investigate the controllability of spin 1 systems and the realization of ternary gates.Using dipole and quadrupole operators as the orthogonal basis of su(3) algebra,we discuss the controllability of one spin 1 systems and offer the concept of a complete set of control operators first.Then we present the controllability of two spin 1 systems coupled with Ising interaction and the transforming relations of the drift process of the system.Finally the specific realization of the ternary SWAP gate in these systems is discussed.It takes 9 drift processes and 25 basic control processes.