Parsimonious and robust realizations of unitary maps in the one-way model

We present a new set of generators for unitary maps over C-2 which differs from the traditional rotation-based generating set in that it uses a single-parameter family of unitaries J(alpha). These generators are implementable in the one-way model [Raussendorf and Briegel, Phys. Rev. Lett. 86, 5188 (2001)] using only two qubits, and lead to both parsimonious and robust implementations of general unitaries. As an illustration, we give an implementation of the controlled-U family which uses only 14 qubits, and has a 2-colorable underlying entanglement graph (known to yield robust entangled states).