$\mathsf{StoqMA}$ captures the computational hardness of approximating the ground energy of local Hamiltonians that do not suffer the so-called sign problem. We provide a novel connection between $\mathsf{StoqMA}$ and distribution testing via reversible circuits. First, we prove that easy-witness $\mathsf{StoqMA}$ (viz. $\mathsf{eStoqMA}$, a sub-class of $\mathsf{StoqMA}$) is contained in $\mathsf{MA}$. Easy witness is a generalization of a subset state such that the associated set's membership can be efficiently verifiable, and all non-zero coordinates are not necessarily uniform. This sub-class $\mathsf{eStoqMA}$ contains $\mathsf{StoqMA}$ with perfect completeness ($\mathsf{StoqMA}_1$), which further signifies a simplified proof for $\mathsf{StoqMA}_1 \subseteq \mathsf{MA}$ [BBT06, BT10]. Second, by showing distinguishing reversible circuits with ancillary random bits is $\mathsf{StoqMA}$-complete (as a comparison, distinguishing quantum circuits is $\mathsf{QMA}$-complete [JWB05]), we construct soundness error reduction of $\mathsf{StoqMA}$. Additionally, we show that both variants of $\mathsf{StoqMA}$ that without any ancillary random bit and with perfect soundness are contained in $\mathsf{NP}$. Our results make a step towards collapsing the hierarchy $\mathsf{MA} \subseteq \mathsf{StoqMA} \subseteq \mathsf{SBP}$ [BBT06], in which all classes are contained in $\mathsf{AM}$ and collapse to $\mathsf{NP}$ under derandomization assumptions.
翻译:$mathfsf{StoqMA}$( Viz. $mathfsf{StoqMA}$[ffs{Stoma}$]$(美元=mathfsff{StoqMA}$) 的计算硬度, 一个不遭受所谓标志问题的本地汉密尔顿人的地面能量近值 $\mathfsf{StoqMA}$的计算硬度。 首先, 我们证明, 简单验证了 $masffsf{StoqMA} 美元(美元=masfff{Stoma}$$) 的计算硬度; 一个完全完整的小类$\math{StoMA} 美元(美元=mas foria}StoqMA} 美元(美元) 。 简单验证了美元=mas=mas=mas a remas demass。