2013/06/30 by Tzu-Chieh Wei · 3 citations
Computer Science · Physics and Astronomy · #Cluster state #Condensed matter physics #Frustration #Lattice (music) #Physics #Quantum #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum computer #Quantum many-body systems #Quantum mechanics #Qubit #Theoretical physics #Universality (dynamical systems) #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreva.88.062307
published as Phys. Rev. A 88, 062307 (2013) · 10 pages, 11 figures, title changed, close to published version
openalex publication_date 2013/12/05 · arxiv created 2013/12/07 · arxiv updated 2013/12/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Universal quantum computation can be achieved by simply performing single-spin measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki (AKLT) states has recently been explored; for example, the spin-1 AKLT chain can be used to simulate single-qubit gate operations on a single qubit, and the spin-3/2 two-dimensional AKLT state on the honeycomb lattice can be used as a universal resource. However, it is unclear whether such universality is a coincidence for the specific state or a shared feature in all two-dimensional AKLT states. Here we consider the family of spin-3/2 AKLT states on various trivalent Archimedean lattices and show that in addition to the honeycomb lattice, the spin-3/2 AKLT states on the square octagon (4,82) and the ``cross'' (4,6,12) lattices are also universal resource, whereas the AKLT state on the ``star'' (3,122) lattice is likely not due to geometric frustration.