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The Complexity of the Local Hamiltonian Problem | | Julia Kempe
; Alexei Kitaev
; Oded Regev
; | | Date: |
24 Jun 2004 | | Subject: | Quantum Physics; Computational Complexity | quant-ph cs.CC | | Abstract: | 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 NP-complete 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 independent proofs; our first proof uses only elementary linear algebra. Our second proof uses a powerful technique for analyzing the sum of two Hamiltonians; this technique is based on perturbation theory and we believe that it might prove useful elsewhere. Using our techniques we also show that adiabatic computation with two-local interactions on qubits is equivalent to standard quantum computation. | | Source: | arXiv, quant-ph/0406180 | | Services: | Forum | Review | PDF | Favorites | |
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