eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-11-04
48
63
10.4230/LIPIcs.TQC.2015.48
article
The Spin-2 AKLT State on the Square Lattice is Universal for Measurement-based Quantum Computation
Wei, Tzu-Chieh
Raussendorf, Robert
One-way quantum computation was first invented using the cluster state. Since then graph states, the generalization of the cluster state, were investigated and understood when they would enable such a measurement-based approach for quantum computation. Are there any other family of states, i.e., states with different entanglement structures, that can also serve as the universal resource for quantum computation? Recent study shows that the Affleck-Kennedy-Lieb-Tasaki (AKLT) states also provide a useful source. Here, we show that the spin-2 state on the square lattice is a universal resource for measurement-based quantum computation. We employ a POVM on all sites that convert the local 5-level system to 2-level, and the post-POVM state is a graph state, whose graph is in general non-planar. We then follow with another round of measurement to recover the planarity of the graphs by thinning. The resultant typical graphs are shown to reside in the supercritical phase of percolation via Monte Carlo simulations and the associated graph states are universal, implying the AKLT state is also universal.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol044-tqc2015/LIPIcs.TQC.2015.48/LIPIcs.TQC.2015.48.pdf
Measurement-based quantum computation
AKLT state
graph state
percolation