Computational difficulty of finding matrix product ground states.

@article{Schuch2008ComputationalDO,
  title={Computational difficulty of finding matrix product ground states.},
  author={Norbert Schuch and J. Ignacio Cirac and Frank Verstraete},
  journal={Physical review letters},
  year={2008},
  volume={100 25},
  pages={
          250501
        }
}
We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians, which are known to be matrix product states (MPS). To this end, we construct a class of 1D frustration-free Hamiltonians with unique MPS ground states and a polynomial gap above, for which finding the ground state is at least as hard as factoring. Without the uniqueness of the ground state, the problem becomes NP complete, and thus for these Hamiltonians it cannot even be certified that the… CONTINUE READING

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