Optimizing Entangling Power and Preserving Circuit Symmetry in Hybrid Quantum Generative Adversarial Networks for Expressive Variational Generation

This work presents a Hybrid Quantum Generative Adversarial Network (HQGAN) that combines symmetry-preserving variational quantum circuits with entangling power optimization, targeting improved expressivity and training stability on NISQ devices. The quantum generator employs layered parameterized circuits composed of Ising-type entangling gates and symmetric single-qubit rotations, inspired by convolutional neural networks. To guide circuit design, we quantify the entanglement capability of each layer using the entangling power (EP) metric via Monte Carlo sampling. Compared to traditional fully connected architectures, HQGAN introduces three major improvements: (1) symmetry-preserving gates preserve translational invariance and enhance feature extraction; (2) modular subcircuit designs with patch-wise outputs reduce parameter overhead by 50\% while improving convergence; (3) optimized entanglement via EP leads to better initialization and performance. Experimental results on Fashion-MNIST and OptDigits demonstrate that HQGAN achieves the same level of fidelity as the original model within 400 epochs,The KL divergence of the entanglement-enhanced Ising-based model is reduced to 0.023, compared to the baseline model. Moreover,parameter complexity is reduced from \( O(N^2) \) to \( O(\mathrm{poly}(N)) \), alleviating overfitting and improving generalization. These results confirm the importance of structure-aware circuit design and entanglement-driven optimization for quantum generative modeling under near-term constraints.