Any n-qubit QC Hamiltonian sparsifies to Õ(n/ε²) terms preserving all state energies within 1±ε using invariant subspace decomposition and the Alon-Kozma operator inequality.
Sparsifying Cayley Graphs on Every Group , booktitle =
3 Pith papers cite this work. Polarity classification is still indexing.
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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.
Every abelian Cayley graph admits an optimal O(ε^{-2} log |G|)-generator weighted Cayley spectral sparsifier, proved via a character-symmetry volume bound on a sparsification polytope.
citing papers explorer
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Quantum Cut Sparsifiers
Any n-qubit QC Hamiltonian sparsifies to Õ(n/ε²) terms preserving all state energies within 1±ε using invariant subspace decomposition and the Alon-Kozma operator inequality.
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Many Hamiltonians Are Sparsifiable
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.
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Optimal Sparsifiers for Abelian Cayley Graphs
Every abelian Cayley graph admits an optimal O(ε^{-2} log |G|)-generator weighted Cayley spectral sparsifier, proved via a character-symmetry volume bound on a sparsification polytope.