As one of the latest fields of interest in both academia and industry, quantum computing has garnered significant attention. Among various topics in quantum computing, variational quantum circuits (VQC) have been noticed for their ability to carry out quantum deep reinforcement learning (QRL). This paper verifies the potential of QRL, which will be further realized by implementing quantum multi-agent reinforcement learning (QMARL) from QRL, especially for Internet-connected autonomous multi-robot control and coordination in smart factory applications. However, the extension is not straightforward due to the non-stationarity of classical MARL. To cope with this, the centralized training and decentralized execution (CTDE) QMARL framework is proposed under the Internet connection. A smart factory environment with the Internet of Things (IoT)-based multiple agents is used to show the efficacy of the proposed algorithm. The simulation corroborates that the proposed QMARL-based autonomous multi-robot control and coordination performs better than the other frameworks.