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.
Morgenstern,Existence and explicit constructions ofq + 1regular Ramanujan graphs for every prime powerq, J
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The authors establish K_KR ≤ 694198146664396294486127753 / 34994834677886019996000000 ≈ 19.837, halving the original Kalton-Roberts upper bound.
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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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Halving the original Kalton--Roberts upper bound for nearly additive set functions
The authors establish K_KR ≤ 694198146664396294486127753 / 34994834677886019996000000 ≈ 19.837, halving the original Kalton-Roberts upper bound.