Optimization of deterministic photonic graph state generation via local operations

Realizing photonic graph states, crucial in various quantum protocols, is challenging due to the absence of deterministic entangling gates in linear optics. To address this, emitter qubits have been leveraged to establish and transfer the entanglement to photons. We introduce an optimization method for such protocols based on the local Clifford equivalency of states and the graph theoretical correlations of the generation cost parameters. Employing this method, we achieve a 50% reduction in use of the 2-qubit gates for generation of the arbitrary large repeater graph states and similar significant reductions in the total gate count for generation of random dense graphs.