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To address the potential threat to the power grid industry posed by quantum computers and ensure the security of bidirectional communication in smart grids, it is imperative to develop quantum-safe authentication protocols. This paper proposes a semi-quantum bidirectional authentication protocol between a control center (CC) and a neighboring gateway (NG). This method uses single photons to facilitate communication between the CC and the NG. Security analysis demonstrates that the protocol can effectively resist common attack methods, including double CNOT attacks, impersonation attacks, interception-measurement-retransmission attacks, and entanglement-measurement attacks. Comparisons with other protocols reveal that this protocol has significant advantages, making it more appealing and practical for real-world applications. Finally, by simulating the protocol on the IBM quantum simulator, this protocol not only validates the theoretical framework but also confirms the practical feasibility of the protocol. [ABSTRACT FROM AUTHOR]