Optimization of deterministic generation of photonic graph states via local operations

Photonic graph states serve as promising resources in various measurement-based quantum computation and communication protocols, such as quantum repeaters. However, their realization with linear optics poses challenges due to the absence of deterministic photon-entangling gates in such platforms. A potential solution involves leveraging quantum emitters, such as quantum dots or NV centers, to establish entanglement and subsequently transfer it to the emitted photons. The design of a quantum circuit that implements the generation of a graph state within such a framework is highly non-trivial nonetheless. Here, we introduce a generation circuit optimization approach that leverages the concept of local equivalency of graphs and employs graph theoretical correlations to explore alternative, cost-effective circuits. Obtaining a 50% reduction in the use of 2-qubit gates for preparing repeater graph states highlights the potential efficacy of our method.