Hamiltonian-Guided Leverage Embedding: Robust Subspace Compression for Efficient QAOA Parameter Estimation

Abstract:Every Ising energy is a known linear function of measured spin features, yet the standard QAOA estimator discards this structure. We introduce Hamiltonian-Guided Leverage Embedding (HGLE), which projects Hamiltonian coefficients onto the leading subspace of a measured feature matrix. The fraction of coefficient norm outside this subspace yields a deterministic, same-batch certificate bounding how much compression distorts the objective. This certificate is minimax-tight - no linear estimator on the same subspace achieves smaller worst-case error. We establish four results beyond the pointwise certificate. First, a held-out pilot projector with summable failure allocation gives population-distortion intervals valid over an unbounded adaptive sequence. Second, coefficient projection strictly reduces estimator variance, with the reduction equal to the variance of the discarded component. Third, one SVD basis simultaneously certifies Kobservables, defeating the rank-1 degeneracy of single-Hamiltonian compression. Fourth, the compression quality is governed by graph topology through the expected Gram matrix.

arXiv:2606.07814 [quant-ph]

(or arXiv:2606.07814v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.07814 Focus to learn more arXiv-issued DOI via DataCite

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