The one-way quantum computer - a non-network model of quantum computation

A one-way quantum computer (QC(C)) works by performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the QC(C). On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the QC(C). In this paper, two examples of the non-network character of the QC(C) are given. First, circuits in the Clifford group can be performed in a single time step. Second, the QC(C)-realization of a particular circuit-the bit-reversal gate-has no network interpretation.