<p>The pattern synthesis of an antenna array is an important component that can improve the effectiveness of a wireless communication system. Achieving low side-lobe levels (SLL) while maintaining excellent directivity is still a major problem for circular antenna arrays (CAA). For real-world applications, there are a number of traditional synthesis techniques available, but they frequently fail to efficiently optimize both parameters at the same time. This paper formulates an optimization problem to optimize directivity, minimize side-lobe levels, and steer the main lobe in a desired direction. In order to achieve these goals, the quantum-based naked mole rat algorithm (QNMRA) is presented. The traditional Naked Mole-Rat Algorithm (NMRA) lacks exploration capabilities and suffers from premature convergence since it uses a deterministic worker update scheme. In order to address these constraints, a quantum-inspired probabilistic position update based on a delta potential well model is proposed, along with a mean-best guidance mechanism and a self-adaptive breeder phase. Initially, the operational efficiency of the suggested QNMRA algorithm has been evaluated and verified using the CEC 2019 numerical benchmark test problems. QNMRA performs better compared to NMRA and other state-of-the-art metaheuristics in Friedman ranking and statistically significant differences. For parameter optimization of the CAA design, in the 12-element CAA case, QNMRA showed a 4.66 dB improvement in the SLL compared to NMRA and shows better convergence stability. In the 24-element setup, the simulation results show that QNMRA performs better with improved directivity and significantly lower SLLs. The findings validate that integration of quantum-inspired mechanisms manifests a significant improvement in exploration-exploitation balance, leading to better optimization precision and stability in the array synthesis problems.</p>