Friday, June 7, 2013

1306.1420 (Tzu-Chieh Wei)

Quantum computational universality of spin-3/2
Affleck-Kennedy-Lieb-Tasaki states on trivalent Archimedean lattices

Tzu-Chieh Wei
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 $(4,8^2)$ and the `cross' $(4,6,12)$ lattices are also universal resource, whereas the AKLT state on the `star' $(3,12^2)$ lattice seems likely not due to geometric frustration.
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