version 2 - 2021-11-17

Optical quantum networks can enable long-range quantum communication and modular quantum computation. A powerful approach is to use multi-qubit network nodes which provide the quantum memory and computational power to perform entanglement distillation, quantum error correction,

and information processing. Nuclear spins associated with optically-active defects in diamond are promising qubits for this role. However, their dephasing during entanglement distribution across the optical network hinders scaling to larger systems. In this work, we show that a single 13C spin in isotopically engineered diamond offers a long-lived quantum memory that is robust to the optical link operation. The memory lifetime is improved by two orders-of-magnitude over the longest reported value, and exceeds the best reported times for making photonic entanglement. We identify ionisation of the NV center as a newly limiting decoherence mechanism. As a first step towards overcoming this limitation, we demonstrate that the nuclear spin state can be retrieved with high fidelity after a complete cycle of ionisation and recapture. Finally, we use numerical simulations to show that the combination of this improved memory lifetime with previously demonstrated entanglement links and gate operations can enable key primitives for quantum networks, such as deterministic nonlocal two-qubit logic operations and GHZ state creation across four network nodes. Our results pave the way for test-bed quantum networks capable of investigating complex algorithms and error correction.