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June 8, 2011 to June 11, 2011
ISBN: 978-0-7695-4411-3
pp: 178-188
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
Sevag Gharibian, Julia Kempe, "Approximation Algorithms for QMA-Complete Problems", CCC, 2011, 2012 IEEE 27th Conference on Computational Complexity, 2012 IEEE 27th Conference on Computational Complexity 2011, pp. 178-188, doi:10.1109/CCC.2011.15
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