  Measurement-based quantum computation describes a scheme where entanglement
of resource states is utilized to simulate arbitrary quantum gates via local
measurements. Recent works suggest that symmetry-protected topologically
non-trivial, short-ranged entanged states are promising candidates for such a
resource. Miller and Miyake [NPJ Quantum Information 2, 16036 (2016)] recently
constructed a particular $\mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2$
symmetry-protected topological state on the Union-Jack lattice and established
its quantum computational universality. However, they suggested that the same
construction on the triangular lattice might not lead to a universal resource.
Instead of qubits, we generalize the construction to qudits and show that the
resulting $(d-1)$ qudit nontrivial $\mathbb{Z}_d \times \mathbb{Z}_d \times
\mathbb{Z}_d$ symmetry-protected topological states are universal on the
triangular lattice, for $d$ being a prime number greater than 2. The same
construction also holds for other 3-colorable lattices, including the
Union-Jack lattice.
