Hybrid valence-bond states for universal quantum computation

The spin-3/2 Affleck-Kennedy-Lieb-Tasaki (AKLT) valence-bond state on the hexagonal lattice was shown to be a universal resource state for measurement-based quantum computation (MBQC). Can AKLT states of higher spin magnitude support universal MBQC? We demonstrate that several hybrid 2D AKLT states involving mixture of spin-2 and other lower-spin entities, such as spin-3/2 and spin-1, are also universal for MBQC. This significantly expands universal resource states in the AKLT family. Even though frustration may be a hinderance to quantum computational universality, lattices can be modified to yield AKLT states that are universal. The family of AKLT states thus provides a versatile playground for quantum computation.