  $\mathsf{StoqMA}$ 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.
