Robert Raussendorf, University of British Columbia
We demonstrate that the two-dimensional AKLT state on a honeycomb lattice is a universal resource for measurement-based quantum computation . Our argument proceeds by reduction of the AKLT state to a 2D cluster state, which is already known to be universal, and consists of two steps. First, we devise a local POVM by which the AKLT state is mapped to a random planar graph state. Second, we show numerically that the connectivity properties of these random graphs are governed by percolation, and that typical graphs are in the connected phase. The corresponding graph states can then be transformed to 2D cluster states by standard techniques.
Joint work with Tzu-Chieh Wei and Ian Affleck. An analogous result has been obtained by A. Miyake in .
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