  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 of an NV centre. The memory lifetime is improved by two
orders-of-magnitude upon the state-of-the-art, and exceeds the best reported
times for remote entanglement generation. We identify ionisation of the NV
centre 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 non-local 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.
