StoqMA vs. MA: the power of error reduction

TL;DR

This paper explores the relationship between StoqMA and MA, showing that if error reduction is possible for StoqMA, then the two classes are equivalent, impacting our understanding of quantum complexity classes.

Contribution

It demonstrates that error reduction for StoqMA implies StoqMA equals MA, addressing an open problem since 2006.

Findings

Error reduction for StoqMA implies StoqMA = MA

Addresses an open problem in quantum complexity theory

Links classical and quantum complexity classes

Abstract

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 BPP, BQP, MA, QMA, etc.,this property remains open for StoqMA since Bravyi, Bessen and Terhal defined this class in 2006. In this note, we show that error reduction forStoqMA will imply that StoqMA = MA.