  The controlled Z (CZ) operations acting separately on pairs of qubits are
commonly adopted in the schemes of generating graph states, the multi-partite
entangled states for the one-way quantum computing. For this purpose, we
propose a setup of cascade CZ operation on a whole group of qubits in sequence.
The operation of the setup starts with entangling an ancilla photon to the
first photon as qubit, and this ancilla automatically moves from one
entanglement link to another in assisting the formation of a string in graph
states. The generation of some special types of graph states, such as the
three-dimensional ones, can be greatly simplified in this approach. The setup
presented uses weak nonlinearities, but an implementation using probabilistic
linear optics is also possible.
