Extended Data Fig. 2: Flowchart of the experimental sequences.

The decision trees of the ADwin microprocessors (Jaeger ADwin Pro II) that create the overarching measurement and control loops for network nodes A and B are shown. Both nodes use arbitrary-waveform generators (AWGs) for microwave and laser pulse sequencing (Tektronix AWG5014C). We additionally use a complex programmable logic device (CPLD) to herald the successful generation of an entangled state in real time (described further in Methods). a, Decision tree when benchmarking the entangled state. b, Deterministic entanglement delivery. Here the ADwin microprocessors keep track of the time since the end of the phase stabilization (t = 0). ‘CR check’: as explained in Extended Data Fig. 1, the NV centre is deemed to be on resonance with the excitation lasers if the number of photons detected during the charge/resonance check surpasses a certain threshold (n_ph > thr); this is repeated until the threshold is passed. ‘comm.’ and ‘comm. timeout’: both ADwin microprocessors exchange classical communication, such as the success of the charge/resonance check, via a three-step-handshake; if one microprocessor waits longer than 1 ms for a response from its counterpart, then the communication times out and we return to the previous logical step (arrow). ‘Count attempts’: the number of entangling attempts N are counted until N = N_max. ‘Count dec. time’: the time since phase stabilization is tracked; if the time is equal to the pre-specified state-generation time t_gen, then the AWG is triggered and the local readout sequences are executed. ‘Wait for basis rot.’: ADwin microprocessors wait for a trigger input from the AWG (‘AWG done’), which indicates that the last microwave rotation before optical readout has been completed. ‘Trigger AWGs’: the microprocessor of node A triggers the AWGs of both nodes to initiate the microwave and entangling sequences; we use a single microprocessor as the trigger source to avoid timing jitter between both generated sequences. ‘SSRO’: optical single-shot readout. ‘Suc.: Trig. from CPLD’ and ‘Fail: Trigger from AWG’: during entanglement generation, the CPLD communicates successful detection of a photon to the nodes; during the single-photon entanglement-benchmarking experiment, the AWG at each node flags failure of the round after 250 entangling attempts. ‘Do stabilize?’: The microprocessors communicate that phase stabilization will be the next step in the experimental sequence; the microprocessor at node A then proceeds with the phase stabilization while that at node B waits until the phase stabilization has finished. The deterministic entangling sequence is run a total of 1,500 times (500 times per readout basis) before a new round is called in, which starts again with the verification of resonant conditions for both NV centres.