The local Hamiltonian problem on a line with eight states is QMA-complete

@article{Hallgren2013TheLH,
  title={The local Hamiltonian problem on a line with eight states is QMA-complete},
  author={Sean Hallgren and Daniel Nagaj and Sandeep Narayanaswami},
  journal={Quantum Inf. Comput.},
  year={2013},
  volume={13},
  pages={721-750}
}
The Local Hamiltonian problem is the problem of estimating the least eigenvalue of a local Hamiltonian, and is complete for the class QMA. The 1D problem on a chain of qubits has heuristics which work well, while the 13-state qudit case has been shown to be QMA-complete. We show that this problem remains QMA-complete when the dimensionality of the qudits is brought down to 8. 

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