Photonic systems are among the most promising for robust quantum information processing. Photonic entangled graph states can be used to encode quantum information in a way that is robust against loss and decoherence, and they serve as a fundamental resource for various quantum applications, e.g., quantum computing, communication and sensing. In this talk, we will present our recent progress toward deterministically generating photonic graph states using quantum emitters. We propose several schemes for generating microwave graph states using transmon qubits, and we provide explicit superconducting circuit designs and fidelity estimates. Furthermore, we will also discuss the required resources for generating photonic graph states deterministically from other types of emitters such as quantum dots or color centers. We will present our algorithm for determining the minimum number of quantum emitters and the precise operation sequence needed to generate an arbitrary target photonic graph state. The algorithm and the operation sequence both scale polynomially in the size of the photonic graph state.
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