Differentiable Energy-Based Regularization in GANs: A Simulator-Based Exploration of VQE-Inspired Auxiliary Losses

This paper presents an exploratory, simulator-based proof of concept investigating whether differentiable energy terms derived from parameterized quantum circuits can serve as auxiliary regularization signals in Generative Adversarial Networks (GANs). We augment the Auxiliary Classifier GAN (ACGAN) generator objective with a Variational Quantum Eigensolver (VQE)-inspired energy term computed from class-specific Ising Hamiltonians using Qiskit's EstimatorQNN and TorchConnector. Important limitations: All experiments run on a noiseless statevector simulator with only 4 qubits, use a deliberately simple Hamiltonian parameterization, and lack ablation studies comparing against equivalent classical biases. The computational overhead (approximately 200x slower than classical ACGAN) reflects simulator artifacts rather than inherent quantum costs. On MNIST, we observe that the energy-regularized model (termed QACGAN) achieves high classification accuracy (99 to 100 percent) within 5 epochs compared to 87.8 percent for ACGAN, suggesting the auxiliary term influences class conditioning. However, sample quality metrics (FID) show high variance across runs (coefficient of variation approximately 25 percent at epoch 5), with values ranging from 19.92 to 35.96. Extended runs stabilize around FID 23 to 24, comparable to the ACGAN baseline. We explicitly do not claim quantum advantage, improved stability in any general sense, or scalability beyond this toy setting. The contribution is methodological: demonstrating that VQE-style energy computations can be integrated into GAN training loops via differentiable pathways. Whether such auxiliary signals provide benefits beyond equivalent classical regularizers remains an open question requiring systematic ablation studies, which we leave for future work.