The Local Consistency Problem for Stoquastic and 1-D Quantum Systems
Abstract
The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known to be QMA-complete. Here we consider special cases of Local Hamiltonian, for ``stoquastic'' and 1-dimensional systems, that seem to be strictly easier than QMA. We show that there exist analogous special cases of Local Consistency, that have equivalent complexity (up to poly-time oracle reductions). Our main technical tool is a new reduction from Local Consistency to Local Hamiltonian, using SDP duality.
Cite
@article{arxiv.0712.1388,
title = {The Local Consistency Problem for Stoquastic and 1-D Quantum Systems},
author = {Yi-Kai Liu},
journal= {arXiv preprint arXiv:0712.1388},
year = {2007}
}
Comments
18 pages, submitted to IEEE Conference on Computational Complexity (CCC). v2: slightly revised introduction