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Center for Nonlinear Studies |
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 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., vol. 58, 1999] to the quantum setting, and might be of independent interest. This is joint work with Julia Kempe. I will attempt to make the talk accessible to both computer scientists and physicists.
Host: Rolando Somma, somma@lanl.gov, 5-5021