Photonic resource state generation from a minimal number of quantum emitters

Abstract Multi-photon entangled graph states are a fundamental resource in quantum communication networks, distributed computing, and sensing. These can principle be created deterministically from emitters such as optically active dots or defects, atomic systems, superconducting qubits. However, finding efficient schemes to produce has been long-standing challenge. Here, we present an algorithm that, given desired multi-photon state, determines the minimum number of precise operation sequences that it. The itself resulting sequence both scale polynomially size photonic allowing one obtain generate containing hundreds thousands photons.