Fault-tolerant quantum computation in concatenation of verified cluster states

A novel scheme is presented for fault-tolerant quantum computation based on the cluster model. Some relevant logical cluster states are constructed in concatenation by post-selection through verification, without necessity of recovery operation, where a suitable code such as the Steane's 7-qubit code is adopted for transversal operations. This simple concatenated construction of verified cluster states achieves a high noise threshold ~1%, and restrains the divergence of resources.