Weaving light-matter qubits into a one way quantum computer

Measurement-based quantum computation has revolutionized quantum information processing, and the physical systems with which it can be implemented. One simply needs the ability to prepare a particular state, known as the cluster state, and subsequently to perform single-qubit measurements on it. Nevertheless, a scalable implementation is yet to be realized. Here we propose a hybrid light-matter system comprised of coupled cavities interacting with two level systems. Utilising the stable, individually addressable, qubits resulting from the localised long-lived atom-photon excitations, we demonstrate how to use the natural system dynamics to `weave' these qubits into a cluster state and propose the implementation of quantum algorithms employing just two rows of qubits. Finally, we briefly discuss the prospects for experimental implementation using atoms, quantum dots or Cooper pair boxes.