Fig. 6: A subcircuit equivalent to a CX_s,p gate, up to a conditional phase correction, for transferring entanglement in our proposed scheme.

This example “emit-then-add” step replaces every pumping gate in typical deterministic schemes for generating arbitrary photonic graph states. Entanglement between a photon (p) and a coherently pumped emitter (e) (represented by a red CX_e,p gate) is exchanged to an auxiliary spin (s) via a two-qubit entangling CZ_e,s gate and local complementation. The emitter is measured out thereafter and reinitialized for the next iteration of the procedure. Rotations about X and Z are by π/2 and −π/2, respectively, as noted in Eq. (13). The measurement of the emitter is with respect to the Z basis. All previously added photons at iterations k < m are unaffected.