title: Universal resources for measurement-based quantum computation.
abstract: We investigate which entanglement resources allow universal measurement-based quantum computation via single-qubit operations. We find that any entanglement feature exhibited by the 2D cluster state must also be present in any other universal resource. We obtain a powerful criterion to assess the universality of graph states by introducing an entanglement measure which necessarily grows unboundedly with the system size for all universal resource states. Furthermore, we prove that graph states associated with 2D lattices such as the hexagonal and triangular lattice are universal, and obtain the first example of a universal nongraph state.
authors.affiliation: Institut für Quantenoptik und Quanteninformation der Osterreichischen, Akademie der Wissenschaften, Innsbruck, Austria.
authors.forename: Maarten
authors.initials: M
authors.lastname: Van den Nest
authors.forename: Akimasa
authors.initials: A
authors.lastname: Miyake
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Dür
authors.forename: Hans J
authors.initials: HJ
authors.lastname: Briegel