An economical route to one-way quantum computation

We assess the effects of a realistic intrinsic model for imperfections in cluster states by introducing noisy cluster states and characterizing their role in the one-way computational model. A suitable strategy to counter-affect these non-idealities is represented by the use of small clusters, stripped of any redundancy, which leads to the search for compact schemes for one-way quantum computation. In light of this, we quantitatively address the behavior of a simple four-qubit cluster which simulates a controlled-NOT under the influences of our model for decoherence. Our scheme can be particularly useful in an all-optical setup and the strategy we address can be directly applied in those, experimental situations where small cluster states can be constucted.