Institute for Quantum Information Seminar
Low-temperature phases of strongly-interacting quantum many-body systems can exhibit a range of exotic quantum phenomena, from superconductivity to fractionalized particles. One exciting prospect is that the ground or low-temperature thermal state of an engineered quantum system can function as a quantum computer. For this idea to be sensible, the usefulness of a ground or low-temperature thermal state for quantum computation cannot be critically dependent on the details of the system's Hamiltonian; if so, engineering such systems would be difficult or even impossible. A much more powerful result would be the existence of a robust ordered phase which is characterised by its ability to perform quantum computation.
I'll discuss some recent results on the existence of such a quantum computational phase of matter, working within the measurement-based (cluster state) model of quantum computation. I will show that the ability to perform certain logic gates such as the identity gate over long distances in the model corresponds precisely to the recently-proposed notion of 'symmetry-protected topological order' for an appropriate symmetry group. Using some techniques from fault-tolerance, we can then prove that any perturbation of the cluster state model will result in a ground state that remains universal for quantum computation, provided the perturbation is sufficiently small and respects a certain symmetry.