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Accurate modeling of electric power transmission networks (EPTNs) is essential for real-time monitoring, operational awareness, and contingency analysis in power systems. Representing EPTNs as graphs with nodes and edges offers a powerful abstraction of the network topology. However, inferring this topology using only phasor measurement unit (PMU) data remains a challenge, especially with no prior network information. In this study, a quantum-classical hybrid approach based on the quantum approximate optimization algorithm (QAOA) to infer a transmission network graph model (TNGM) directly from PMU data is presented. The proposed approach utilizes a cost function incorporating the difference between power mismatch and mean power loss to guide one-to-one branch matching. Furthermore, the effect of quantum circuit depth is investigated to achieve 100% accuracy in TNGM construction. Typical results are presented on the two-area four-machine power system.