HMB-GAN: Hybrid Multi-B\'ezier GAN for Vector Shape Synthesis

We explore the use of hybrid quantum-classical generative adversarial networks for synthesising CAD-ready vector geometries. Unlike prior work that operates in rasterised or single-B\'ezier domains, we introduce HMB-GAN (Hybrid Multi-B\'ezier GAN), an end-to-end differentiable generative framework that constructs closed shapes through stitched multi-segment B\'ezier representations with geometric continuity enforced by construction. We compare a quantum-enhanced generator with a classical generator within this architecture and evaluate them across point cloud distribution metrics and geometric shape statistics. Results show that despite faster convergence, a reduction in model parameter count, and slightly improved performance on point cloud metrics, the quantum generator suffers from excessive simulator overhead and thus classically-simulated evaluation suffers from hardware constraints. These results demonstrate the feasibility of modelling structured geometries through hybrid quantum architectures whilst highlighting contemporary hardware limitations.