# Analysis of Quantum-Classical Hybrid Deep Learning for 6G Image Processing with Copyright Detection
## 4 Simulation Analysis
It begins at approximately 0.025 s and experiences two notable peaks: the first and highest at 0.27 s just before the 60 th simulation, and a second peak of 0.24 s around the 65 th simulation. After these peaks, the quantum model's execution time decreases, eventually returning to levels close to its starting point. In contrast, while following a similar trend, the classical model generally maintains lower execution times than the quantum model. Interestingly, it exhibits a peak that coincides with the quantum model's second peak around the 65 th simulation. This synchronization suggests that both models may be responding to similar computational challenges at this point in the simulation sequence. Overall, Figure 3 demonstrates that while both models show variability in execution times, the quantum model consistently requires slightly more computational time, with more pronounced peaks compared to the classical model. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameter** & **Current Value** & **Optimization Range** & **Description** \\ \hline _n_qubits_ & 3 & 2–8 & Number of qubits in quantum circuit \\ \hline _n\_timesteps_ & 50 & 20–200 & Number of time steps in simulation \\ \hline _n\_iterations_ & 5 & 1–20 & Number of optimization iterations per time step \\ \hline _n\_spatial\_configs_ & 3 & 1–10 & Number of spatial configurations \\ \hline _ZZFeatureMap_ reps & 1 & 1–5 & Repetitions in quantum feature map \\ \hline _RealAmplitudes_ reps & 1 & 1–5 & Repetitions in variational form \\ \hline _Optimization step scale_ & 0.5 & 0.1–2.0 & Scale in norm.pdf for optimization step \\ \hline _Network fluctuation amplitude_ & 0.1 & 0.01–0.5 & Amplitude of network fluctuation \\ \hline _Network fluctuation frequency_ & 0.05 & 0.01–0.2 & Frequency of network fluctuation \\ \hline _Network noise scale_ & 0.05 & 0.01–0.2 & Scale of random noise in network fluctuation \\ \hline _Probability update rate_ & 0.8 & 0.5–0.95 & Weight for current state in probability update \\ \hline _Network impact on probability_ & 0.01 & 0.001–0.1 & Impact of network fluctuation on probability \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameter list. Figure 2: Second comparative results of the quantum and classical models in our 6C network simulation. Figure 4 compares the average execution times between the quantum and classical models over 100 simulations. The bar graph illustrates a notable difference in computational efficiency between the two approaches. The quantum model, on average, requires 0.07 s per simulation, which is significantly higher than the classical model's average of 0.048 s. This difference of approximately 0.022 s per simulation indicates that the classical model consistently outperforms the quantum model in terms of execution speed. The higher average execution time for the quantum model aligns with the trends observed in Figure 3, where the quantum simulations generally showed higher execution times throughout the simulation range. This comparison in Figure 4 quantifies the overall performance difference, suggesting that the classical approach offers a computational speed advantage for this particular 6G network simulation scenario. The results highlight an important consideration in the practical application of quantum versus classical algorithms in network simulations, where execution time can be a critical factor in real-world implementations. Figure 4: Average execution time comparison between quantum and classical (100 simulations). Figure 3: Execution times for each simulation with averages. Figure 5 illustrates the average expected cost over time for both the quantum and classical models, spanning from time step 0 to 50. The graph reveals distinct cost profiles for each approach, while also highlighting some similarities in their overall patterns. The quantum model, represented by the blue line, begins with a higher average expected cost of approximately 1.5 and concludes at around 1.4. It exhibits a smooth oscillating pattern throughout the period, with gentle rises and falls.