Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice

TL;DR

This paper demonstrates that certain spin-3/2 AKLT states on various two-dimensional lattices serve as universal resources for measurement-based quantum computation, extending known universality beyond the honeycomb lattice.

Contribution

It shows that spin-3/2 AKLT states on multiple trivalent lattices are universal resources, revealing that universality is not limited to the honeycomb lattice.

Findings

AKLT states on square octagon and cross lattices are universal resources.

AKLT state on star lattice is likely not universal due to geometric frustration.

Universality extends beyond the honeycomb lattice to other trivalent lattices.

Abstract

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 is likely not due to geometric frustration.