2004/08/04 by Maarten Van den Nest, Akimasa Miyake, Wolfgang Dür +3 · 9 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Cluster state #Combinatorics #Computation #Computer science #Graph #Lattice (music) #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum computer #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Qubit #Statistical physics #Theoretical computer science #Topology (electrical circuits) #Universality (dynamical systems) #quant-ph
paper · pdf · doi:10.1103/physrevlett.97.150504
published as Phys. Rev. Lett. 97, 150504 (2006) · 4 pages, 1 figure; final version
openalex publication_date 2004/08/04 · arxiv created 2006/10/16 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/11
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.