论文标题
Chernoff的光谱限制为当地哈密顿人的简短证明
Short proof of a spectral Chernoff bound for local Hamiltonians
论文作者
论文摘要
我们简单地证明了Chernoff限制了基于Weyl的不平等现象的$ K $ - 本地Hamiltonian。因此，估算频谱的$ε（n）$ - 量子到恒定相对误差的复杂性，因此表现出以下二分法：对于$ε（n）= d^{ - n} $，问题是NP-HARD甚至QMA-HARD，甚至可能存在常量的$ a> 1 $，因此问题对于$ a> $ a> np a> np-a> np-a>。我们注意到，由于Kuwahara和Saito（Ann。Phys。20）的一般性问题，相关的Chernoff束缚也足以建立这种二分法，其证明依赖于对\ emph {cluster膨胀}的仔细分析。
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 \emph{cluster expansion}.
