Energy saving has become a critical challenge in 5G and beyond networks. The rapid growth of connected devices has increased the overall network energy demand, driving operational expenditure to unsustainable heights. The Base Station (BS) accounts for the largest share of energy usage, typically consuming around 60-70\% of the Radio Access Network (RAN)'s total energy. Therefore, to address this issue, this article optimizes the BS's energy usage while accounting for the dynamic behavior of User Equipment (UE). Deep Reinforcement Learning (DRL) is a natural candidate for determining effective energy saving policies, such as automatically switching BSs on or off when user density is low or adjusting transmission power to balance energy efficiency and Quality of Service (QoS). However, its heavy training burden and the exponential growth of state and action spaces in dense 5G environments make exploration increasingly difficult. To overcome these limitations, we introduce a novel Quantum Reinforcement Learning (QRL) algorithm that leverages quantum principles, including superposition and entanglement, through parameterized quantum circuits, enabling significantly faster convergence than DRL, which relies on conventional deep neural networks. Extensive simulations demonstrate that the proposed QRL can substantially reduce energy consumption while maintaining QoS, even when UEs are highly dynamic and frequently switch their association with BS antennas. Additionally, QRL consistently outperforms DRL and Q-Learning in both convergence speed and learning complexity.

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