Tailoring single-chip photonics to single-emitter-based photonic graph state generation

Photonic graph states are a class of entangled many-body states with applications from fundamental quantum physics to all-photonic networks and fusion-based quantum computation. Generating them from single-photon sources poses theoretical and experimental challenges, including photon indistinguishability, which can be improved by minimizing the number of quantum emitters. The time-delayed feedback protocol addresses this by using a single quantum emitter, a mediator system (typically an atom in a cavity), and delay lines to enable indirect photon interactions. While experimentally efficient, this setup requires careful tuning of emitter and mediator cavity parameters to ensure high-fidelity state generation. In this work, we analyze the collective performance of the emitter and mediator in this protocol. We demonstrate a fidelity-rate tradeoff as a function of the emitter cavity’s Purcell enhancement for both time-bin and polarization encodings. We then show how the mediator’s parameters can be optimized, relative to the emitter’s, to enable high-fidelity indirect photon interactions. Optimal performance occurs when the mediator’s Purcell enhancement is much larger than the emitter’s. Finally, we examine how the joint emitter–mediator design impacts photon loss, indistinguishability, and Bell-state measurement error rates. Our results inform the single-chip implementation of time-delayed feedback protocols for scalable photonic graph state generation.