  We show that the NP complete problems MAX CUT and INDEPENDENT SET can be
formulated as the 2-local Hamiltonian problem as defined by Kitaev. He
introduced the quantum complexity class BQNP as the quantum analog of NP, and
showed that the 5-local Hamiltonian problem is BQNP-complete. It is not known
whether the s-local Hamiltonian problem is BQNP-complete for s smaller than 5.
Therefore it is interesting to determine what problems can be reduced to the
s-local Hamiltonian problem. Kitaev showed that 3-SAT can be formulated as a
3-local Hamiltonian problem. We extend his result by showing that 2-locality is
sufficient in order to encompass NP.
