Abstract
Based on the former structures in the generation of two-dimensional cluster states, we first propose a scheme to generate linear three-dimensional (3D) cluster state. After that, we develop the former structures to three-dimension, and then we could use them to generate universal 3D cluster states. In final, we provide two new structures, which could make the generation of a special type of 3D cluster state very efficient. All the proposals work with cross-phase modulation, so they are deterministic, highly efficient, fast, compared with the former schemes. It will make the requirement of quantum memory much relax, thus it is more feasible and suitable for large-scale one-way quantum computation.
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