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Entanglement is a crucial resource for quantum information processing, and soprotocols to generate high fidelity entangled states on various hardwareplatforms are in demand. While spin chains have been extensively studied togenerate entanglement, graph structures also have such potential; however, onlya few classes of graphs have been explored for this specific task. In thispaper, we apply a particular coupling scheme involving two different couplingstrengths to a graph of two interconnected $3\times3$ square graphs such thatit effectively contains three defects. We show how this structure allowsgeneration of a Bell state whose fidelity depends on the chosen coupling ratio.We apply partitioned graph theory in order to reduce the dimension of the graphand show that, using a reduced graph or a reduced chain, we can still simulatethe same protocol with identical dynamics. Finally, we investigate howfabrication errors affect the entanglement generation protocol and how thedifferent equivalent structures are affected, finding that for some specificcoupling ratios they are extremely robust.

Generation and Robustness of Quantum Entanglement in Spin Graphs