## 1 Introduction  
Recent years have seen a worldwide interest in Wireless Sensor Network (WSN) [1] technology, which has been considered one of the most promising technologies in smart manufacturing. Actually, the development tendency of WSN is in accordance with its context of Industry 4.0 [2]. Together with the Industrial Internet, the Internet of Things (IoT) [3], whose kernel is WSN, contributes to the achievement of the connectivity and communication of Cyber-Physical Systems (CPS) [4]. WSN techniques are appropriate for long-term data acquisition for IoT representation in an industrial environment.  
WSNs are distinguished from traditional wireless networks by their dissimilar purposes: WSNs are data-centric, while the latter aim for data transmission. In traditional wireless networks, such as Ad hoc and Wireless Local Area Networks (WLANs), the main task is to find the low-latency path between the source node and the destination node, and to improve the utilization of the whole network in order to avoid communication congestion and simultaneously balance network flow. However, in WSNs, a routing method has two main functions: to find the optimal path from the source node to the destination node, and to transmit a data packet along that path. The main aim of network routing improvement is to extend network life and prevent connection errors [5]. The routing method's emphasis is on energy efficiency, because of limited node energy and long lifetime requirements. Meanwhile, since the number of sensor nodes tends to be very large, and these nodes can only obtain local topological information, a suitable route should be chosen by considering local network information.  
Since the network is resource- and power-limited, general wireless communication network routing methods are not well-suited for WSNs, especially in industrial fields in which there is demand for high performance in energy efficiency and longevity. Accordingly, some routing approaches have emerged, such as swarm intelligence-based schemes [5; 6]. Social insect colonies, such as those of ants and honeybees [7; 8], have complex collective behaviors and decentralized management structures, which are similar to parallel, dynamic, and distributed systems. Researchers have studied ant colony optimization (ACO)-based routing schemes to develop high-performance routing methods [9].  
In order to improve the limitations of ACO-based routing methods, such as earlier stagnation and slow astringency, this paper considers the idea of using quantum-inspired evolutionary algorithms (QEAs) [10; 11] and ACO together, balancing load, real-time transmission, and energy consumption with a multi-objective fitness function. A novel and efficient routing approach for WSNs, called the Quantum Ant Colony Multi-Objective Routing (QACMOR) algorithm, is proposed accordingly. In QACMOR, some quantum computing mechanisms of QEAs, including the quantum bit (qubit) and the quantum rotation gate, are introduced into ACO. The former represents the node's pheromone, and the latter updates it. QEAs are able to avoid premature convergence with a simple implementation, which has more potential for solving large-scale problems than do other general evolutionary algorithms. In multiple objectives, more attention is paid to computation speed by using the look-up table of the rotation angle of QEAs and setting a time-delay factor in fitness function.  
The rest of the paper is organized as follows: Section 2 presents the literature review on WSN routing methods. Section 3 sheds light on ACO-based routing in detail. Section 4 explains the proposed QACMOR approach. Section 5 shows the experimental results of performance evaluation and case study validated in a continuous steel casting production line. Finally, Section 6 discusses conclusions and future work.