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Thursday, May 22, 2014
12:30 PM - 2:00 PM
T-DO Conference Room

Quantum Lunch

Quantum computational universality of Affleck-Kennedy-Lieb-Tasaki states on two-dimensional lattices

Tzu-Chieh Wei
Stony Brook University

Universal quantum computation can be achieved by simply performing single-spin measurements on a highly entangled resource state, such as 2D cluster states. So far there is no complete characterization of universal resource states for measurement-based quantum computation. The family of Affleck-Kennedy-Lieb-Tasaki (AKLT) states has recently been explored in this context; 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 AKLT states on various two-dimensional lattices. We demonstrate 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 resources, whereas the AKLT state on the `star' $(3,12^2)$ lattice is likely not due to geometric frustration. Moreover, certain AKLT states with spin-2 and lower spin mixture are also universal.

Host: Rolando Somma