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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Witness Set for simple polygons is in NP ∩ XP and admits an n^{f(k)}-time algorithm via combinatorial discretization, in contrast to its ∃R-complete dual.
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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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Witness Set: A Visibility Problem in $NP\cap XP$
Witness Set for simple polygons is in NP ∩ XP and admits an n^{f(k)}-time algorithm via combinatorial discretization, in contrast to its ∃R-complete dual.