Year: 2006
Type: article
Abstract: The k-{\locHam} problem is a natural complete problem for the complexity class $\QMA$, the quantum analogue of $\NP$. It is similar in spirit to {\sc MAX-k-SAT}, which is $\NP$-complete for $k\geq 2$. It was known that the problem is $\QMA$-complete for any $k \geq 3$. On the other hand, 1-{\locHam} is in {\P} and hence not believed to be $\QMA$-complete. The complexity of the 2-{\locHam} 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 2-local interactions on qubits is equivalent to standard quantum computation.
Source: SIAM Journal on Computing
Authors: Julia Kempe, Alexei Kitaev, Oded Regev
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2793525843