Multidimensional cluster states using a single spin-photon interface coupled strongly to an intrinsic nuclear register

Cathryn P. Michaels, Jesús Arjona Martínez, Romain Debroux, Ryan A. Parker, Alexander M. Stramma, Luca I. Huber, Carola M. Purser, Mete Atatüre, and Dorian A. Gangloff

Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, UK

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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.

Quantum states composed of multiple entangled photons are a key resource in quantum computing networks, both for robust communication and for implementing computational tasks. Photonic cluster states whose entanglement is multidimensional are required for universal quantum protocols. Such cluster states can be obtained from a highly efficient single-photon source, together with entangling gates between distinct emitters or between local spins. We propose to use the multidimensional entanglement naturally available to a single diamond colour center strongly coupled to an intrinsic nuclear spin to create multi-dimensional cluster states of photons. Our simulations show that 100-photon cluster states are realisable within achievable experimental parameters.

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