  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.
