# Analysis of Quantum-Classical Hybrid Deep Learning for 6G Image Processing with Copyright Detection
## 3 Methodology  
Our methodology employs a comprehensive simulation framework designed to model the dynamic conditions of 6G networks, incorporating key features such as ultra-high bandwidth, extremely low latency, and network fluctuations. Within this simulated environment, we implement and compare quantum-enhanced deep learning models, including quantum neural networks (QNNs) and the Quantum Approximate Optimization Algorithm (QAOA), against classical deep learning approaches such as convolutional neural networks (CNNs) and generative adversarial networks (GANs). The models are evaluated across various network fluctuation scenarios, including bandwidth variations, latency changes, and node failures, to assess their performance and adaptability in processing complex image data under challenging 6G conditions. We utilize a diverse set of images processing tasks, including classification, segmentation, and generation, to comprehensively evaluate the models' capabilities. Performance metrics such as accuracy, processing speed, and resource utilization are carefully measured and analyzed to thoroughly compare quantum and classical approaches in the context of 6G network environments. These equations represent key aspects of our simulation framework for comparing quantum and classical deep learning approaches in 6G network environments. Network fluctuation equations are employed in our simulation to accurately model the dynamic nature of 6G environments, capturing variations in bandwidth and latency that are characteristic of next-generation wireless networks. These equations allow us to test the robustness and adaptability of both quantum and classical deep learning models under realistic, changing network conditions, providing insights into their performance in future 6G deployments. A simple model for network fluctuations can be represented as  
\[B(t)=B_{0}+\Delta B\cdot\sin(\omega t)\]  
where the following definitions hold:  
\(B(t)\) is the bandwidth at time \(t\). \(B_{0}\) is the base bandwidth. \(\Delta B\) is the amplitude of fluctuation. \(\omega\) is the frequency of fluctuation. \[P(a)=|\langle a|\psi\rangle|^{2}\]  
where the following definitions hold:  
\(P(a)\) is the probability of measuring outcome \(a\). \(|\,a\rangle\) is the eigenstate corresponding to outcome \(a\). \(|\,\psi\rangle\) is the state of the system. To compare the performance of quantum and classical models, one can use a metric like  
\[Relative\;Quantum\;Advantage\;=\;\frac{Quantum_{Performance}\;-\;Classical_{ Performance}}{Classical_{Performance}}\]  
This simulation compares quantum and classical deep learning approaches for image processing in a dynamic 6G network environment, implementing quantum circuits and classical neural networks to process image-like data over multiple time steps and spatial configurations. The quantum model utilizes a quantum feature map and variational circuit,while the classical model employs Gaussian filtering and simple neural network processing. Network fluctuations are simulated using a combination of sinusoidal functions and random noise, creating a dynamic environment that mimics the variability expected in 6G networks. The simulation tracks and compares the performance of both models by monitoring the evolution of probability distributions, expected costs, and adaptability to network fluctuations. Through comprehensive visualization of results, including probability distribution evolution and expected cost comparisons, the simulation provides valuable insights into the potential advantages and limitations of quantum and classical approaches in future 6G network scenarios. The Algorithm 1 for simulating quantum and classical models in 6G networks is structured to evaluate their performance across various metrics, utilizing input parameters such as the number of qubits (_n_qubits_), the size of the input data (_n_pixels_), the number of time steps (_n_timesteps_), optimization iterations (_n_iterations_), spatial configurations (_n_spatial_configs_), and total simulations (_n_simulations_).