Stephen Bartlett gave a colloquium on this topic today.
The ground states of quantum antiferromagnets contain substantial amounts of entanglement (although how much is hard to quantify). Hence, one might hope they are a resource that might be used in quantum computation. Stephen described some recent work [see this PRL and this PRL ] which considers how this might be done. The focus seems to be on gapped systems which have hidden symmetries and can be described as tensor network states. The prime example is the Haldane spin-1 antiferromagnetic Heisenberg chain which is adiabatically connected to the AKLT model.
I was reminded of some work I was involved in a few years ago (described in this PRL) which showed how one could take any spin singlet state [not just the ground state!] from a spin-1/2 chain and perform projective Bell measurements (on pairs of spins) along the chain and teleport quantum states with perfect fidelity along the chain. I was wondering what the relationship (similarities and differences) of our work was with this more recent work.