# Analysis of Quantum-Classical Hybrid Deep Learning for 6G Image Processing with Copyright Detection
## 4 Simulation Analysis
In contrast, the classical model, depicted by the orange line, starts at a much lower cost of about 0.5 and ends slightly lower at 0.4. The classical model also displays a similar undulating pattern, mirroring the quantum model's trends but at a consistently lower cost level. Notably, both models show comparable patterns of fluctuation after their initial starting points, suggesting they respond similarly to changes in the simulation environment over time. However, the most striking feature of this graph is the significant and persistent gap between the two models' cost profiles. The quantum model maintains a substantially higher average expected cost throughout the entire simulation period, consistently about 1.0 units above the classical model. This visualization demonstrates that while both models evolve similarly over time, the classical approach consistently achieves a lower average expected cost in this 6G network simulation scenario. The simulation comparing quantum and classical approaches in 6G network optimization reveals intriguing trends as quantum advantage increases. In the execution time analysis, the quantum model demonstrates significant improvement, with its execution time decreasing from 0.016 s at no advantage to 0.008 s at a quantum advantage of 2.0. Conversely, the classical model maintains a consistent execution time of 0.0117 s throughout, unaffected by the quantum advantage parameter. This trend indicates that as quantum technology advances, it has the potential to surpass classical methods in computational speed for certain network optimization tasks. The speedup factor, which compares the execution times of the two models, further illustrates this trend. Starting at 0.7 when there is no quantum advantage, it rises steadily to 1.4 at a quantum advantage of 2.0. This progression demonstrates that the quantum model transitions from being slower than the classical model to significantly faster as the quantum advantage increases. The point where the speedup factor crosses 1.0 marks the threshold at which the quantum model begins to outperform the classical model in terms of execution speed. Figure 5: Average expected cost over time between quantum and classical models. When examining the average cost of solutions, we observe a notable improvement in the quantum model's performance as quantum advantage increases. The quantum model's average cost starts at 1.5 with no advantage and decreases to 0.8 at a quantum advantage of 2.0. In contrast, the classical model maintains a constant average cost of 0.5 throughout the simulation. This trend suggests that while the quantum model's solution quality is improving with increased quantum advantage, it has not yet matched the efficiency of the classical model in this particular optimization scenario. The cost ratio, calculated by dividing the quantum model's cost by the classical model's cost, provides a clear picture of the relative efficiency of the two approaches. Starting at 2.95 when there is no quantum advantage, the cost ratio decreases to 1.5 at a quantum advantage of 2.0. This significant reduction indicates that the quantum model is becoming increasingly competitive with the classical model in terms of solution quality. However, the fact that the ratio remains above 1.0 even at the highest simulated quantum advantage suggests that further technological advancements may be necessary for quantum methods to fully match or surpass classical methods in solution quality for this specific 6G network optimization task. These simulation results paint a nuanced picture of the potential for quantum computing in 6G network optimization. As quantum advantage increases, we see clear improvements in both execution speed and solution quality for the quantum model. The quantum approach transitions from being significantly slower to notably faster than the classical approach while substantially closing the gap in solution quality.