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The 2-local Hamiltonian problem encompasses NP

Pawel Wocjan·Thomas Beth
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Abstract

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.

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Pawel Wocjan, Thomas Beth. 2003-01-17. The 2-local Hamiltonian problem encompasses NP. https://arxiv.org/abs/quant-ph/0301087

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