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

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.

10 pages, 11 figures, title changed, close to published version

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Cited by in corpus (16)

• Hierarchy of universal entanglement in 2D measurement-based quantum computation
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Symmetry-protected topologically ordered states for universal quantum computation
• Measurement-Based Quantum Computation
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Hybrid valence-bond states for universal quantum computation
• Quantum spin systems for measurement-based quantum computation
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
• AKLT models on decorated square lattices are gapped
• Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Spectral properties for a family of two-dimensional quantum antiferromagnets
• The AKLT models on the singly decorated diamond lattice and two degree-4 planar lattices are gapped