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But in existing MDQC protocols, the verifiability that clients should verify whether the server executed the protocol correctly and gave correct results was not handled. Therefore, in this paper, we improve a typical MDQC protocol to enable clients to verify the correctness of computation by inserting trap qubits and develop a novel method to enforce clients to send qubits honestly while avoiding the positions of trap qubits being leaked to the server. The security and verifiability of the improved MDQC protocol are also analyzed. 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