Abstract
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 nontrivial, short-ranged entangled states are promising candidates for such a resource. Miller and Miyake [npj Quantum Inf. 2, 16036 (2016)] recently constructed a particular 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 qudit nontrivial symmetry-protected topological states are universal on the triangular lattice, for being a prime number greater than 2. The same construction also holds for other 3-colorable lattices, including the Union Jack lattice.
16 More- Received 7 November 2017
DOI:https://doi.org/10.1103/PhysRevA.97.022305
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