Cybersecurity concerns have arisen due to extensive information exchange among networked smart grid devices which also employ seamless firmware update. An outstanding issue is the presence of malware-injected malicious devices at the grid edge which can cause severe disturbances to grid operations and propagate malware on the power grid. This paper proposes a cloud-based, device-specific malware file detection system for smart grid devices. In the proposed system, a quantum-convolutional neural network (QCNN) with a deep transfer learning (DTL) is designed and implemented in a cloud platform to detect malware files targeting various smart grid devices. The proposed QCNN algorithm incorporates quantum circuits to extract more features from the malware image files than the filter in conventional CNNs and the DTL method to improve detection accuracy for different types of devices (e.g., processor architecture and operating systems). The proposed algorithm is implemented in the IBM Watson Studio cloud platform that utilizes IBM Quantum processor. The experimental results validate that the proposed malware file detection method significantly improves the malware file detection rates compared to the conventional CNN-based method.