@inproceedings{Kempe2004TheCO,
title={The Complexity of the Local Hamiltonian Problem},
author={Julia Kempe and Alexei Y. Kitaev and Oded Regev},
booktitle={FSTTCS},
year={2004}
}

The k-LOCAL HAMILTONIAN problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX-k-SAT, which is NPcomplete for k ≥ 2. It was known that the problem is QMA-complete for any k ≥ 3. On the other hand 1-LOCAL HAMILTONIAN is in P, and hence not believed to be QMA-complete. The complexity of the 2-LOCAL HAMILTONIAN problem has long been outstanding. Here we settle the question and show that it is QMA-complete. We provide two… CONTINUE READING

van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev. Adiabatic quantum computation is equivalent to standard quantum computation. In Proc. 45th FOCS, pages 42–51 • 2004

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J. Kempe, A. Kitaev, O. Regev. The complexity of the local hamiltonian pro Proc