Decrypting chaotic visual ciphers via quasi quantum neural networks (Q²NNs)

We propose a novel Quasi Quantum Neural Network (Q²NN) architecture that integrates classical convolutional networks with variational quantum circuits to decrypt grayscale images encrypted via a multilayer chaotic cryptosystem. This hybrid framework addresses the limitations of classical models when applied to highly nonlinear, permutation-diffusion encrypted data. Q²NN adopts a dual-branch encoder-decoder design, comprising a classical convolutional autoencoder and a variational quantum subnetwork, fused via an adaptive, learnable module that unifies classical and quantum representations. For evaluation, we implement a custom encryption pipeline combining Arnold Cat Map-based spatial permutation, Logistic Map-based pixel-level diffusion, and zigzag chaotic transformations. These operations produce ciphertexts that are key-sensitive, structurally obfuscated, and statistically complex, presenting a significant challenge for conventional decryption models. Leveraging supervised training with known ciphertext-plaintext pairs, Q²NN approximates an inverse mapping from the encrypted domain back to the original image space by co-learning in a joint classical–quantum feature space. Experimental validation on the MNIST dataset demonstrates near-perfect decryption fidelity (MSE < 0.004; SSIM > 0.96), outperforming classical and quantum-only baselines. The underlying chaotic encryption scheme further shows strong cryptographic resilience, with Shannon entropy ≈ 7.96, NPCR > 99.5%, UACI ≈ 33.3%, and negligible spatial correlation. These results highlight the potential of Q²NNs for secure and explainable image decryption, and point to promising directions for hybrid intelligent cryptographic systems in the post-quantum era.