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.
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BibTeX
@misc{mukherjee2026hamiltonianguided,
title = {{Hamiltonian-Guided Leverage Embedding: Robust Subspace Compression for Efficient QAOA Parameter Estimation}},
author = {Sumanta Mukherjee and Kalyan Dasgupta and Surya Shravan Kumar Sajja and Kameshwaran Sampath and Abhishek Singh and Dhriti Verma and Dzung Phan and Jayant Kalagnanam},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.07814},
eprint = {2606.07814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.07814},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hamiltonian-Guided Leverage Embedding: Robust Subspace Compression for Efficient QAOA Parameter Estimation
AU - Sumanta Mukherjee
AU - Kalyan Dasgupta
AU - Surya Shravan Kumar Sajja
AU - Kameshwaran Sampath
AU - Abhishek Singh
AU - Dhriti Verma
AU - Dzung Phan
AU - Jayant Kalagnanam
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2606.07814
UR - https://arxiv.org/abs/2606.07814
AB - 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.
ER -