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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Faster quantum algorithm outputs a state whose energy is at most the minimum energy among all depth-d circuits applied to |0>, plus an energy estimate, for k-local Hamiltonians.
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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An Entropy-Governed Speedup for Quantum Algorithms on Local Hamiltonians
Faster quantum algorithm outputs a state whose energy is at most the minimum energy among all depth-d circuits applied to |0>, plus an energy estimate, for k-local Hamiltonians.