Resource-efficient loss-aware photonic graph state preparation using atomic emitters

Abstract: Multi-qubit entangled photonic graph states are an important ingredient for all-photonic quantum computing, repeaters and networking. Preparing them using probabilistic stitching of single photons using linear optics presents a formidable resource challenge due to multiplexing needs. Quantum emitters provide a viable solution to prepare photonic graph states as they enable deterministic production of photons entangled with emitter qubits, and deterministic two-qubit interactions among emitters. A handful of emitters often suffice to generate useful-size graph states that would otherwise require millions of emitters used as single photon sources, using the linear-optics method. Photon loss however impedes the emitter method due to a large circuit depth, and hence loss accrual on the photons of the graph state produced, given the typically large number of slow two-qubit CNOT gates between emitters. We propose an algorithm that can trade the number of emitters with the graph-state depth, while minimizing the number of emitter CNOTs. We apply our algorithm to generate a repeater graph state (RGS) for a new all-photonic repeater protocol, which achieves a far superior rate-distance tradeoff compared to using the least number of emitters needed to generate the RGS. Yet, it needs five orders of magnitude fewer emitters than the multiplexed linear-optics method -- with each emitter used as a photon source -- to achieve a desired rate-distance performance.