Entangled photon factory: How to generate quantum resource states from a minimal number of quantum emitters

Multi-photon 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. We will present a general algorithm for determining how to generate arbitrary photonic graph states using minimal resources. Starting from a target graph state, this algorithm determines the minimal number of emitters needed to produce it and reverse-engineers explicit operation sequences on the emitters that yield the state. This is done by leveraging the stabilizer formalism, entanglement entropy, and time-reversed operations. The algorithm itself and the resulting emission circuit both scale polynomially in the size of the photonic graph state, allowing one to obtain efficient schemes to generate graph states containing hundreds or thousands of photons.