Parsimonious and robust realizations of unitary maps in the one-way model
Vincent Danos, Elham Kashefi, Prakash Panangaden · Physical Review A · 2005
We present a new set of generators for unitary maps over ${\mathbb{C}}^{2}$ which differs from the traditional rotation-based generating set in that it uses a single-parameter family of unitaries $J(\ensuremath{\alpha})$. 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).