Efficient Photonic Graph State Generation

Graph states are central resources for quantum information processing, supporting applications in computation, communication, and error correction. In photonic systems, they are typically assembled from smaller entangled states using probabilistic fusion gates, which demand many photons and suffer from low success rates. We present an optimized scheme for directly generating caterpillar graph states (CGSs) -- essential resource states for constructing high-dimensional lattice graph states -- using only single-photon sources, linear optics, and heralded measurements. Based on the linear quantum graph (LQG) picture, our method produces CGSs efficiently and scalably. For CGSs of length $l\ge 3$, it requires $l-2$ fewer photons and achieves a success rate $2^{l-2}$ times higher than fusion-based approaches. These results demonstrate that the LQG picture provides a powerful and flexible route for realizing complex photonic graph states with minimal resources.