• Corpus ID: 222140868

# StoqMA vs. MA: the power of error reduction

```@article{Aharonov2020StoqMAVM,
title={StoqMA vs. MA: the power of error reduction},
author={Dorit Aharonov and Alex Bredariol Grilo and Yupan Liu},
journal={ArXiv},
year={2020},
volume={abs/2010.02835}
}```
• Published 6 October 2020
• Computer Science
• ArXiv
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.
4 Citations
StoqMA meets distribution testing
• Yupan Liu
• Mathematics, Computer Science
TQC
• 2021
This work proves that easy-witness \$\mathsf{StoqMA}\$ 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, and makes a step towards collapsing the hierarchy.
The Complexity of Translationally Invariant Problems beyond Ground State Energies
• Mathematics
ArXiv
• 2020
This work shows that the translationally invariant versions of both APX-SIM and GSCON remain intractable, and gives a framework for lifting any abstract local circuit-to-Hamiltonian mapping \$H\$ (satisfying mild assumptions) to hardness of APx-SIM on the family of Hamiltonians produced by \$H\$, while preserving the structural and geometric properties of \$H \$ (e.g. translation invariance, geometry, locality, etc).
On polynomially many queries to NP or QMA oracles
• Computer Science, Mathematics
Electron. Colloquium Comput. Complex.
• 2021
This work shows that for any veriﬁcation class C, any P C machine with a query graph of “separator number” s can be simulated using deterministic time exp, and shows how to combine Gottlob’s “admissible-weighting function’ framework with the “ﬂag-qubit” framework for embedding P C computations directly into APX-SIM instances in a black-box fashion.
Termwise versus globally stoquastic local Hamiltonians: questions of complexity and sign-curing
• Physics
• 2020
We elucidate the distinction between global and termwise stoquasticity for local Hamiltonians and prove several complexity results. We show that the stoquastic local Hamiltonian problem is

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