# Analysis of Quantum-Classical Hybrid Deep Learning for 6G Image Processing with Copyright Detection
## 3 Methodology
It initializes essential functions for calculating costs, managing network fluctuations, performing optimization steps, and processing probabilities. The simulation begins with an outer loop for the number of simulations, initializing timing variables and histories to track performance metrics. Within this loop, an inner loop iterates over spatial configurations, setting uniform probability distributions for both models. At each time step, the algorithm measures execution times while calculating costs for the quantum model and generating random images for the classical model. It computes network fluctuations, updates probabilities through optimization steps based on costs and fluctuations and processes these probabilities independently. If not at the initial time step, it updates and normalizes probabilities based on previous states. The current probabilities and expected costs are stored for later analysis. After all simulations are complete, the algorithm returns cumulative execution times and expected cost histories for both models. Post-simulation analysis includes calculating average execution times, analyzing probability distribution evolution, plotting expected costs over time, and visualizing network fluctuations to provide insights into each model's adaptability and performance. Overall, this framework offers a comprehensive approach to comparing quantum and classical methods in optimizing 6G network performance, paving the way for further research into advanced computational techniques in telecommunications. The key difference between the quantum and classical approaches lies in their respective cost functions and how they evolve their probability distributions over time. The quantum model computes quantum circuits, while the classical model uses traditional computing methods. Algorithm: Quantum-Classical-Classical Cost Function Optimization Simulation. The simulation focuses on optimizing the performance of quantum and classical models in 6G networks by leveraging cost functions that guide the optimization process. The quantum cost function evaluates how well a quantum state meets specific criteria, such as energy levels or conservation laws, by incorporating penalty terms that enforce desired properties. This function is crucial for minimizing the expectation value of a Hamiltonian, thereby optimizing the quantum state. In contrast, the classical cost function quantifies the performance of classical algorithms by measuring discrepancies between predicted and actual outcomes, often in tasks like error minimization in machine learning models. By iteratively updating probabilities based on these cost functions, the simulation aims to enhance routing optimization and resource allocation within the network. This hybrid approach not only accelerates convergence to optimal solutions but also demonstrates the potential advantages of integrating quantum computing into telecommunications, paving the way for more efficient and scalable 6G network designs. ```
**Input**: the number of qubits, the number of qubits that is 2 raised to the power of n, the number of time steps in the simulation, the number of optimization iterations per time step, the number of spatial configurations, and the number of times to run the full simulation. **Output**: the average execution times for quantum and classical models, the probability distribution evolution for both models, and the expected cost over time for both models.