2011 IEEE 26th Annual Conference on Computational Complexity (2011)
San Jose, California USA
June 8, 2011 to June 11, 2011
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.15
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.
approximation algorithms, QMA-complete, local Hamiltonian, exhaustive sampling
S. Gharibian and J. Kempe, "Approximation Algorithms for QMA-Complete Problems," 2011 IEEE 26th Annual Conference on Computational Complexity(CCC), San Jose, California USA, 2011, pp. 178-188.