Short Proof of a Spectral Chernoff Bound for Local Hamiltonians
summary
Claims that the spectral measure of any local Hamiltonian concentrates exponentially in the number of qubits N (not in the number of edges M), with typical deviations of order 1/√N. Proof computes constant moments as tr(H^p) in time N^p, then split hypergraph into matchings and apply classical Chernoff per color so each color gives concentration; combine with eigenvalue inequalities. No randomness or average-case assumption; matches recent De Palma et al. result but with a simpler proof.
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chapters (6)
- 0:00Start
- 1:29Many-body quantum system with local Hamiltonian
- 2:31APPROXIMATION SETTING
- 3:38More approximation: bulk behavior
- 5:39Algorithm yields trivial histogram
- 7:58Exponential spectral concentration bound . Consider g-regular graph. Potentially g 1
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