  Photonic GHZ states serve as the central resource for a number of important
applications in quantum information science, including secret sharing, sensing,
and fusion-based quantum computing. The use of photon-emitter entangling gates
is a promising approach to creating these states that sidesteps many of the
difficulties associated with intrinsically probabilistic methods based on
linear optics. However, the efficient creation of high-fidelity GHZ states of
many photons remains an outstanding challenge due to both coherent and
incoherent errors during the generation process. Here, we propose an
entanglement concentration protocol that is capable of generating perfect GHZ
states using only local gates and measurements on imperfect weighted graph
states. We show that our protocol is both efficient and robust to incoherent
noise errors.
