StoqMA vs. MA: the power of error reduction

Quantum 9, 1853 (2025).

https://doi.org/10.22331/q-2025-09-11-1853

$sf{StoqMA}$ 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 $sf{StoqMA = MA}$.