“…The operators with one particle interactions can be implemented by a sequence of operators of selective z rotations in the following way: (10) for integer spins I, where and (11) for half integer spins I. For the squares of one particle operators for integer spins I, we obtain (13) for half integer spins I, we have (14) Operators with two particle interactions, (15) are constructed by combining several intervals of free evolution under Hamiltonian (1), whose lengths are multiples of periods 2π/q 1 , 2π/q 2 , 2π/ω 1 , and 2π/ω 2 , and the sets of operators of 180 degree y rotations. For such lengths, only the contribution of the spin-spin interaction remains in the evolution operator: (16) Both operators (15) and (16) are represented by diag onal matrices with matrix elements in the form of exponential functions exp(-iΦ m ), m = 1, 2, …, d 1 d 2 , with different phases.…”