Transitions in the computational power of thermal states for   measurement-based quantum computation
  We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct "phases" - one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical or quantum, in the underlying spin-lattice model. 
Sean D. Barrett, Stephen D. Bartlett, Andrew C. Doherty, David   Jennings, and Terry Rudolph