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How to generate photonic cluster state or graph state efficiently is the mainproblem in optical measurement-based quantum computation. Assisted by the crossphase modulation technique, we propose an efficient scheme to realize thecascade CZ operation, which could be used to generate universal cluster state,with the controlled-path gate as element operation. Especially, for the wheelcluster state, the generation processes are obviously simpler than the formerapproaches. Moreover, we consider the artificial error that one forgot tooperate one or some single photons during the generation processes cross-type,star-type graph state. This error likely occurs in the large scale of graphstate generation with one-by-one pattern and is firstly considered in thispaper. With the present approach, it is possible to judge whether all theinvolved single photons are connected as desired or not, i.e., detect theartificial error with the success probability 1/2.

Efficient graph state generation and artificial error detection