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Open Quantum Systems Decoherence
Quantum Simulation
Short proof of a spectral Chernoff bound for local Hamiltonians
arXiv
Authors: Nilin Abrahamsen
Year
2020
Paper ID
20799
Status
Preprint
Abstract Read
~2 min
Abstract Words
106
Citations
N/A
Abstract
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 ε(n)-th quantile up to constant relative error thus exhibits the following dichotomy: For ε(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 ε(n)=a-n. We note that a related Chernoff bound due to Kuwahara and Saito (Ann. Phys. '20) for a generalized problem is also sufficient to establish such a dichotomy, its proof relying on a careful analysis of the cluster expansion.
Why This Paper Matters
- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We give a simple proof of a Chernoff bound for the spectrum of a k-local Hamiltonian based on Weyl's inequalities.
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