  Quantum simulation of a Hamiltonian H requires unitary operator decomposition
(UOD) of its evolution operator, ($U=exp(-i H t)$) in terms of experimentally
preferable unitaries. Here, using Genetic Algorithm optimization, we
numerically evaluate the most generic UOD for the Hamiltonian, DM interaction
in the presence of Heisenberg XY interaction, $H_{DH}$. Using these
decompositions, we studied the entanglement dynamics of Bell state in the
Hamiltonian $H_{DH}$ and verified the entanglement preservation procedure by
Hou et al. [Annals of Physics 327, 292 (2012)].
