StoqMA vs. MA: the power of error reduction

Abstract

$\sf{StoqMA}$ characterizes the computational hardness of stoquastic local Hamiltonians, which is a family of Hamiltonians that does not suffer from the sign problem. Although error reduction is commonplace for many complexity classes, such as $\sf{BPP, BQP, MA, QMA}$, etc.,this property remains open for $\sf{StoqMA}$ since Bravyi, Bessen and Terhal defined this class in 2006. In this note, we show that error reduction for $\sf{StoqMA}$ will imply that $\sf{StoqMA = MA}$.