The Internet of Things (IoT) plays a pivotal role in modern society, connecting everyday objects to the internet and enabling smart functionalities that enhance efficiency, convenience, and sustainability across multiple sectors. As IoT networks have expanded in scale and complexity, optimising energy consumption has become critical to ensuring their long-term sustainability and cost-effectiveness. This paper introduces quantum-inspired particle swarm optimisation clustering (QIPSOC), an innovative metaheuristic that relies on a novel mathematical formulation (MPMC) and integrates principles from quantum computing and particle swarm optimisation to achieve energy-efficient clustering, balancing network performance constraints and energy consumption. By encoding particles as n-qubit systems and employing quantum-inspired motion through qubit rotations along with an inertial damping factor, QIPSOC enhances solution diversity, mitigates premature convergence to local optima, and guides the exploration of the solution space to achieve significant energy savings, ranging from 17.99 % to over 91 %, depending on the network configuration. These results underscore QIPSOC's superiority over state-of-the-art methods in optimising energy efficiency and performance in IoT networks, making it well-suited for real-world deployment scenarios requiring rapid decision-making.