Photonic cluster states are a powerful resource for measurement-based quantum computing and loss-tolerant quantum communication. Proposals to generate multi-dimensional lattice cluster states have identified coupled spin-photon interfaces, spin-ancilla systems, and optical feedback mechanisms as potential schemes. Following these, we propose the generation of multi-dimensional lattice cluster states using a single, efficient spin-photon interface coupled strongly to a nuclear register. Our scheme makes use of the contact hyperfine interaction to enable universal quantum gates between the interface spin and a local nuclear register and funnels the resulting entanglement to photons via the spin-photon interface. Among several quantum emitters, we identify the silicon-29 vacancy centre in diamond, coupled to a nanophotonic structure, as possessing the right combination of optical quality and spin coherence for this scheme. We show numerically that using this system a 2×5-sized cluster state with a lower-bound fidelity of 0.5 and repetition rate of 65 kHz is achievable under currently realised experimental performances and with feasible technical overhead. Realistic gate improvements put 100-photon cluster states within experimental reach.

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We propose the generation of multi-dimensional cluster states using a single, efficient spin-photon interface coupled strongly to a nuclear register. We show numerically that for SiV- in diamond a 2×5- sized cluster state is achievable.

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