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A Hamiltonian-Guided Pre-Trainer for Variational Quantum Algorithms
DescriptionThe optimization of variational quantum algorithms (VQAs) is notoriously challenging due to poor parameter initialization, which often traps optimizers in suboptimal local minima. Existing methods rely on a static guessing paradigm that is fundamentally limited. This paper presents a Hamiltonian-guided pre-trainer (HGP), a new approach that dynamically constructs a better starting point. HGP iteratively refines parameters by performing exact global optimization within low-dimensional subspaces. These subspaces are identified using a Hamiltonian-guided parameter blocking strategy, and the optimization is achieved by reconstructing the analytic landscape from a few quantum measurements via a Fast Fourier Transform. We evaluated HGP on canonical spin models, where it consistently produced superior starting points for standard optimizers. Ablation studies reveal Hamiltonian-guided parameter blocking reduces the initial energy error by nearly 30-fold versus the next best benchmark. These results highlight the importance of Hamiltonian guided pre-training for enhancing VQA performance.