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.
Code sparsification and its applications
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
representative citing papers
Symmetric Boolean CSP predicates of arity at most 5 have their non-redundancy NRD_n(R) classified as O(n^t) for small t, with all arity-4 cases and all but two arity-5 cases resolved via t-balancedness and OR-reductions.
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.
Introduces strong sparsification for 1-in-3-SAT by merging variables, relying on a sub-quadratic vector-set bound derived from the Polynomial Freiman-Ruzsa Theorem, with an application to hypergraph coloring approximation.
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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Non-Redundancy of Low-Arity Symmetric Boolean CSPs
Symmetric Boolean CSP predicates of arity at most 5 have their non-redundancy NRD_n(R) classified as O(n^t) for small t, with all arity-4 cases and all but two arity-5 cases resolved via t-balancedness and OR-reductions.
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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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Strong Sparsification for 1-in-3-SAT via Polynomial Freiman-Ruzsa
Introduces strong sparsification for 1-in-3-SAT by merging variables, relying on a sub-quadratic vector-set bound derived from the Polynomial Freiman-Ruzsa Theorem, with an application to hypergraph coloring approximation.
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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.