Our work addresses the problem of generating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin–Meshkov–Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2s have modelled a wide range of problems in physics. Here, we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis $\{|j = 1,\mu\langle; \mu = + 1, 0, -12\}$. Our technique relies on the decomposition of a Hamiltonian in terms of $SU$(3) basis matrices. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of $SU(n)$ generators. These matrices are constructed out of angular momentum operators J$_x$, J$_y$, J$_z$. We construct and study the properties of perfect entanglers acting on a symmetric subspace, i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.