Robust and parsimonious realisations of unitaries in the one-way model

Abstract

We present a new set of generators for unitary maps over \otimes^n(C^2) which differs from the traditional rotation-based generating set in that it uses a single-parameter family of 1-qubit unitaries J(a), together with a single 2-qubit unitary controlled-Z. Each generator is implementable in the one-way model using only two qubits, and this leads 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-colourable underlying entanglement graph (known to yield robust entangled states).