Neural-network-encoded Variational Quantum Algorithms

Variational quantum algorithms (VQAs) are typically optimized instance by instance, making them measurement-expensive on noisy intermediate-scale quantum (NISQ) hardware. We present neural-network-encoded VQAs (NNVQAs), where a classical neural network maps Hamiltonian parameters directly to the parameters of a parameterized quantum circuit, enabling amortized inference: a single pretrained model can provide accurate circuit parameters for an entire family of related problem instances without per-instance optimization. We realize this idea with a neural-network-encoded VQE (NNVQE) for parameterized 1D and 2D XXZ spin models, achieving accurate ground-state energy estimates across phases and generalizing to previously unseen parameter settings. We also employ an active-learning strategy to reduce the number of training instances while maintaining prediction accuracy, thereby lowering total measurement cost. Our results indicate a practical hybrid workflow in which training is performed once (on high-quality hardware) and inference is deployed broadly to resource-limited end users.