# Analysis of Quantum-Classical Hybrid Deep Learning for 6G Image Processing with Copyright Detection
## 4 Simulation Analysis  
Figure 1 illustrates the comparative results of the quantum and classical models in our 6G network simulation. As a result of the simulation, we can observe distinct differences between the quantum and classical models in their probability distribution evolution. The quantum model exhibits an evenly distributed pattern of higher probability solution indices over time. In contrast, the classical model consistently shows higher probabilities for specific pixel indices from time step 10 to 50, with a few lower probability indices unevenly distributed elsewhere. This suggests that the classical model tends to converge on particular solutions, while the quantum model maintains a more diverse set of potential solutions. The expected cost comparison further highlights these differences, with the quantum model's costs ranging from 2.2 to 3.5, significantly higher than the classical model's range of 0.1 to 0.5. This indicates that the classical model achieves lower expected costs despite its more focused solution approach. Both models operate within the same network environment, characterized by fluctuations ranging from \(-0.05\) to 0.20 over time,  
as shown in the bottom panel of Figure 1. These results reveal the trade-offs between the two approaches: the quantum model's broader exploration of the solution space comes at a higher cost, while the classical model's more targeted approach yields lower costs but potentially less diverse solutions. Figure 2 presents another set of simulation results, showing slight variations from the previous findings while maintaining overall similar patterns. In this iteration, the quantum model continues to demonstrate an evenly distributed probability across solution indices over time, consistent with its behavior in Figure 1. The classical model, however, exhibits a more pronounced tendency towards constant probability distributions, with only a few exceptions deviating from this pattern. This reinforces the observation that the classical approach converges more strongly on specific solutions, while the quantum approach maintains a broader exploration of the solution space. The expected cost comparisons and network fluctuations remain largely unchanged from the previous simulation, with the quantum model still showing higher costs ranging from approximately 2.2 to 3.5 and the classical model maintaining lower costs in the range of 0.1 to 0.5. The network fluctuations continue to affect both models equally, varying between \(-0.05\) and 0.20. These results further emphasize the consistent difference in behavior between quantum and classical approaches in this 6G network simulation environment, highlighting the trade-off between solution diversity and cost efficiency. This parameter optimization shown in Table 1 provides a comprehensive framework for fine-tuning the quantum-classical comparison simulation in a 6G network environment. It encompasses key variables affecting both the quantum and classical models and the network simulation itself, offering a range of values to explore for each parameter. By systematically adjusting these parameters within their specified ranges, researchers can identify optimal configurations that enhance the performance and adaptability of both quantum and classical approaches in dynamic network conditions. This optimization process allows for a more nuanced understanding of each model's strengths and limitations, potentially revealing scenarios where quantum approaches may offer significant advantages over classical methods in 6G network applications. Figure 1: First simulation of comparative results of the quantum and classical models in our 6G network simulation. Figure 3 illustrates the execution times for each simulation, comparing the quantum and classical models as the number of simulations increases. The graph reveals distinct patterns for both approaches. The quantum model, represented by the blue line, consistently shows slightly higher execution times throughout the simulation range.