2012 IEEE 27th Conference on Computational Complexity (2011)

San Jose, California USA

June 8, 2011 to June 11, 2011

ISSN: 1093-0159

ISBN: 978-0-7695-4411-3

pp: 178-188

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.15

ABSTRACT

Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and initiate its study. We present two main results. The first shows that a non-trivial approximation ratio can be obtained in the class NP using product states. The second result (which builds on the first one), gives a polynomial time (classical) algorithm providing a similar approximation ratio for dense instances of the problem. The latter result is based on an adaptation of the "exhaustive sampling method" by Arora et al. [J. Comp. Sys. Sci. 58, p.193 (1999)] to the quantum setting, and might be of independent interest.

INDEX TERMS

approximation algorithms, QMA-complete, local Hamiltonian, exhaustive sampling

CITATION

Sevag Gharibian,
Julia Kempe,
"Approximation Algorithms for QMA-Complete Problems",

*2012 IEEE 27th Conference on Computational Complexity*, vol. 00, no. , pp. 178-188, 2011, doi:10.1109/CCC.2011.15