# Quantum PSO-Based Optimization of Secured IRS-Assisted Wireless-Powered IoT Networks
## 4 Results and Discussion  
This section highlights the proposed method's effectiveness in a WPIN as supported by our analysis and experimental findings. The numerical results were derived from 100 channel realizations. MATLAB R2022 was utilized to perform simulations over approximately 100 iterations on a system powered by an AMD Ryzen 5 5600X 6-Core CPU operating at 3.70 GHz with 12 threads. A distance-dependent path loss channel model was employed where \(|h|=10^{-3}d^{-\alpha}g\), with \(g\) representing small-scale channel gain, and \(\alpha\) the path loss exponent. The channel gain follows a Rayleigh fading distribution with a mean of zero and unit variance. The maximum transmit power at the base station (\(P_{l}\)) was set to 30 dBm, path loss exponent \(\alpha\) was set to 3, energy harvesting efficiency \(\zeta_{k}=\zeta=0.8\), and noise variance was \(\sigma^{2}=-70\,\mathrm{dBm}/\mathrm{Hz}\). IoT users were evenly distributed within a range of one to five meters from the base station. Figure 4 depicts a convergence graph that illustrates the performance of the QPSO algorithm for various numbers of users (\(K=2\), 4, 8, and 10) over 100 iterations. The fitness values plotted against the number of iterations demonstrate that the algorithm converges quickly, with all scenarios stabilizing within the first 20 iterations. As the number of users increases, the algorithm achieves higher fitness values, with \(K=10\) reaching the highest fitness at approximately 35, while \(K=2\) converges at around 15. This trend indicates that increasing the number of users enhances the performance of the optimization process, likely due to the user density. The algorithm's stability is evident because the fitness values remain constant after convergence, confirming that QPSO efficiently finds optimal solutions early in the iterative process, particularly for large user counts. These results highlight the effectiveness of QPSO in optimizing fitness functions in scenarios with varying user density to improve network performance. Figure 5 shows the relationship between sum secrecy throughput and the number of users \(K\) for different numbers of IRS element \(N\). It is evident that as \(K\) increases, sum secrecy throughput also improves, particularly with the growth in the number of IRS elements \(N\). For \(K\) = 10, the sum secrecy throughput increases from 10 bps/Hz to 13 bps/Hz, resulting in a 30% improvement as \(N\) increases from 10 to 40. Overall, an increasing trend can be seen for all values of \(K\) and \(N\), which suggests that incorporating IRS elements enhances the communication environment, leading to significant improvements in secrecy throughput with an increasing number of users. Figure 6 describes sum secrecy throughput versus the number of users \(K\) across four different optimization scenarios: the proposed QPSO and bisection method, QPSO (phase-optimal), standard PSO, and fixed time, random phase. For \(K\) = 5, the proposed method achieves 18.8 bps/Hz, representing a 9% improvement over the phase-optimal method (17.3 bps/Hz), an 11% improvement compared to standard PSO (16.9 bps/Hz),  
Figure 4: Convergence performance of QPSO with respect to various numbers of users \(K\). Figure 5: Secrecy throughput for different values of users \(K\) and IRS elements \(N\). and a 27% improvement in comparison to fixed time, random phase (14.8 bps/Hz). The results indicate an increasing trend in secrecy throughput as the number of users increases, with the proposed QPSO and bisection method demonstrating the highest performance. This is due to the joint optimization of phase shift and time allocation, outperforming QPSO with phase-only optimization and the standard PSO approach. Conversely, the fixed-time, random phase scenario exhibited minimal performance in terms of sum secrecy throughput enhancement.