Abstract: Multi-photon entangled graph states are a fundamental resource in quantum communication networks, distributed quantum computing, and sensing. These states can in principle be created deterministically from quantum emitters such as optically active quantum dots or defects, atomic systems, or superconducting qubits. However, finding efficient schemes to produce such states has been a long-standing challenge. I will present an algorithm that, given a desired multi-photon graph state, determines the minimum number of quantum emitters and specific quantum circuits that can produce it. I will then describe heuristic methods to minimize the number of emitter-emitter entangling gates in the circuits, which are the most expensive resource in deterministic state generation protocols.