Extended Data Fig. 1: Deterministic entanglement-delivery sequences.

Pulse sequences for each step of the deterministic entanglement delivery protocol are shown. These sequences are also used in the single-photon entanglement-generation experiment. (1) Optical phase stabilization. Bright light is input to measure and stabilize the interferometer (see Methods). The duration is different for the single-photon entanglement experiment. (2) NV-centre state check. By shining in two lasers that are together resonant with transitions from all of the ground states, the NV centre will fluoresce regardless of its ground-state occupation. By counting photons emitted by the NV centre we can verify that both NV centres are in the desired charge state NV⁻ and that they are on resonance with the applied lasers. The NV centre is deemed to be on resonance if the number of photons detected during the charge/resonance check surpasses a certain threshold. If no photons are detected, then the NV centre is assumed to be in the NV⁰ state and a resonant laser is applied to reset it to NV⁻. (3) Heralded single-photon entanglement generation. Entanglement generation proceeds by optically re-pumping the spins to \(\left|\uparrow \right\rangle \) (including passive charge-state stabilization; see Methods) before a microwave (MW) pulse is used to create the desired bright-state population α at each node. A resonant excitation pulse then generates spin–photon entanglement. A subsequent microwave π pulse is used to ensure that the NV-centre state is refocused before the next stage should success be heralded. (4) Dynamical decoupling. Microwave pulses are used to implement dynamical decoupling (see Methods). (5) Single-shot readout. The NV-centre nodes can be read out in arbitrary bases in a single shot. If required, a microwave pulse is applied to rotate the qubit state before a resonant laser is applied. Fluorescence photons from the NV centre are detected if it is in the state \(\left|\uparrow \right\rangle \).