  We study an effective spin model derived perturbatively from random
transverse-field Ising model on the pyrochlore lattice. The model consists of
spin-configurations on the pyrochlore lattice, restricted to the spin-ice
subspace, with spins interacting with random Ising exchange couplings as well
as ring exchanges along the hexagons of the lattice. This model is studied by
exact diagonalization upto N=64 site systems. We calculate spin-glass
correlation functions and local entanglement entropy $S_T$ between spins in a
single tetrahedron and the rest of the system. We find that the model undergoes
two phase transitions. At weak randomness the model is in a quantum spin-ice
phase where $S_T=\ln{6}$. Increasing randomness first leads to a frozen phase,
with long-range spin-glass order and $S_T=\ln{2}$ corresponding to the Cat
states associated with Ising order. Further increase in randomness leads to a
random resonating-hexagon phase with a frozen backbone of spins and a broad
distribution of entanglement entropies. The implications of these studies for
non-Kramers rare-earth pyrochlores are discussed.
