  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 procedures, which use
either interacting quantum emitters or efficient spin-photon interface, have
been proposed to create these photonic graph states deterministically. 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 hybridizing
quantum-emitter-based graph state generation with all-photonic fusion gates to
produce graph states of complex topology near-deterministically. Our results
should pave the way towards the practical implementation of resource-efficient
quantum information processing, including measurement-based quantum
communication and quantum computing.
