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Simple and deterministic spectral concentration bound for local Hamiltonians
(pp1310-1318)
Nilin Abrahamsen doi:
https://doi.org/10.26421/QIC23.15-16-4 Abstracts: We give a simple proof of a Chernoff
bound for the spectrum of a $k$-local
Hamiltonian based on Weyl's
inequalities. The complexity of estimating the spectrum's $\epsilon(n)$-thquantile
up to constant relative error thus exhibits the following dichotomy: For
$\epsilon(n)=d^{-n}$
the problem is NP-hard and maybe even QMA-hard,
yet there exists constant $a>1$
such that the problem is trivial for $\epsilon(n)=a^{-n}$.
Key Words:
Concentration bounds, local
Hamiltonians
