Near-deterministic hybrid generation of arbitrary photonic graph states using a single quantum emitter and linear optics

Since linear-optical two-photon gates are inherently probabilistic, measurement -based implementations are particularly well suited for photonic platforms: a large highly-entangled photonic resource state, called a graph state, is consumed through measurements to perform a computation. The challenge is thus to produce these graph states. Several generation proce-dures, which use either interacting quan-tum emitters or efficient spin-photon in-terface, have been proposed to create these photonic graph states deterministi-cally. Yet, these solutions are still out of reach experimentally since the state-of-the-art is the generation of a linear graph state. Here, we introduce near -deterministic solutions for the generation of graph states using the current quantum emitter capabilities. We propose hybridiz-ing quantum-emitter-based graph state generation with all-photonic fusion gates to produce graph states of complex topol-ogy near-deterministically. Our results should pave the way towards the prac-tical implementation of resource-efficient quantum information processing, includ-ing measurement-based quantum commu-nication and quantum computing.