We present results illustrating the construction of three-dimensional (3D) topological cluster states with coherent state logic. Such a construction would be ideally suited for wave-guide implementations of optical quantum information processing. We investigate the use of a deterministic controlled- Z gate, showing that given large enough initial cat states, it is possible to build large 3D cluster states. We model X and Z basis measurements by displaced photon number detections and x -quadrature homodyne detections, respectively. We investigate whether teleportation can aid in cluster state construction and whether this introduction of located loss errors fits within the topological cluster state framework.
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Myers et al. (2011) studied this question.
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