  We consider the integrable XXZ model with special open boundary conditions
that renders its Hamiltonian ${SU(2)}_q$ symmetric, and the one-dimensional
quantum Ising model with four different boundary conditions. We show that for
each boundary condition the Ising quantum chain is exactly given by the Minimal
Model of integrable lattice theory $LM(3, 4)$. This last theory is obtained as
the result of the quantum group reduction of the XXZ model at anisotropy
$\Delta=(q + q^{-1})/2=\sqrt{2}/2$, with a number of sites in the latter
defined by the type of boundary conditions.
