Greedy vector balancing on finite unit-vector sets T in R^d achieves norm bound (2/δ_T)^{d-1} independent of sequence length n.
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3 Pith papers cite this work, alongside 317 external citations. Polarity classification is still indexing.
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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.
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.
citing papers explorer
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Greedy Vector Balancing
Greedy vector balancing on finite unit-vector sets T in R^d achieves norm bound (2/δ_T)^{d-1} independent of sequence length n.
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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.