We elucidate the distinction between global and termwise stoquasticity for local Hamiltonians and prove several complexity results. We show that the stoquastic local Hamiltonian problem is $\textbf{StoqMA}$-complete even for globally stoquastic Hamiltonians. We study the complexity of deciding whether a local Hamiltonian is globally stoquastic or not. In particular, we prove $\textbf{coNP}$-hardness of deciding global stoquasticity in a fixed basis and $\Sigma_2^p$-hardness of deciding global stoquasticity under single-qubit transformations. As a last result, we expand the class of sign-curing transformations by showing how Clifford transformations can sign-cure a class of disordered 1D $XYZ$ Hamiltonians.

翻译：我们明确了全球与当地汉密尔顿人之间在时间和时间上的宽度的区别,并证明了一些复杂的结果。我们证明,即使对于全球的宽度汉密尔顿人来说,局部汉密尔顿人的问题也是 $\ textbf{StoqMA}$的完整。我们研究了确定本地汉密尔顿人是否具有全球宽度的复杂程度。特别是,我们证明,固定地决定全球宽度的难度是$\ textbf{coNP}$的硬性,在单方位变换中决定全球宽度的硬性是$\Sigma_2 ⁇ p$。最后,我们通过展示克里夫特变形如何能标志一个1D XYZ$的无序型汉密尔密尔顿人。