@article {1423, title = {The Local Consistency Problem for Stoquastic and 1-D Quantum Systems}, year = {2007}, month = {2007/12/10}, 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 {\textquoteleft}{\textquoteleft}stoquastic{\textquoteright}{\textquoteright} 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. }, url = {http://arxiv.org/abs/0712.1388v2}, author = {Yi-Kai Liu} }