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.
@article{arxiv.0807.4797,
title = {Transitions in the computational power of thermal states for measurement-based quantum computation},
author = {Sean D. Barrett and Stephen D. Bartlett and Andrew C. Doherty and David Jennings and Terry Rudolph},
journal= {arXiv preprint arXiv:0807.4797},
year = {2009}
}