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Although it is well known that all quantum states can be produced by singlequbit measurements on the cluster states, it is not a simple task to explicitlyfind which measurement patterns on the cluster states can generate differentquantum states. In this paper we introduce a general scheme to find measurementpatterns corresponding to different topological CSS states containing Kitaev'storic code states and color code states on different lattices and in differentdimensions. Furthermore, we find a measurement pattern for generating nonabelian anyons where measurement induced defects on a toric code state play therole of Ising anyons. We also support our scheme by a graphical notation where,by following a few simple graphical transformations, one will be able toconvert a CSS topological state to a cluster state. Our scheme can be also usedfor experimental realization of anyons on cluster states.

General scheme for preparation of different topological states on the cluster states