Many r-local Hamiltonians, including Pauli strings, random high-rank operators, and high-rank operators, admit sparsifications with o(n^r) terms that (1±ε)-approximate the original Hamiltonian on all states.
and Teng, Shang-Hua , title =
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Spectral sparsification preserves GNN embedding geometry up to O(ε) perturbations in filters, representations, Gram matrices, and training trajectories.
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Spectral Graph Sparsification Preserves Representation Geometry in Graph Neural Networks
Spectral sparsification preserves GNN embedding geometry up to O(ε) perturbations in filters, representations, Gram matrices, and training trajectories.