TY - GEN
T1 - The complexity of the separable hamiltonian problem
AU - Chailloux, André
AU - Sattath, Or
PY - 2012/9/26
Y1 - 2012/9/26
N2 - In this paper, we study variants of the canonical Local Hamiltonian problem where, in addition, the witness is promised to be separable. We define two variants of the Local Hamiltonian problem. The input for the Separable Local Hamiltonian problem is the same as the Local Hamiltonian problem, i.e. a local Hamiltonian and two energies a and b, but the question is somewhat different: the answer is YES if there is a separable quantum state with energy at most a, and the answer is NO if all separable quantum states have energy at least b. The Separable Sparse Hamiltonian problem is defined similarly, but the Hamiltonian is not necessarily local, but rather sparse. We show that the Separable Sparse Hamiltonian problem is QMA(2)-Complete, while Separable Local Hamiltonian is in QMA. This should be compared to the Local Hamiltonian problem, and the Sparse Hamiltonian problem which are both QMA-Complete. To the best of our knowledge, Separable Sparse Hamiltonian is the first non-trivial problem shown to be QMA(2)-Complete.
AB - In this paper, we study variants of the canonical Local Hamiltonian problem where, in addition, the witness is promised to be separable. We define two variants of the Local Hamiltonian problem. The input for the Separable Local Hamiltonian problem is the same as the Local Hamiltonian problem, i.e. a local Hamiltonian and two energies a and b, but the question is somewhat different: the answer is YES if there is a separable quantum state with energy at most a, and the answer is NO if all separable quantum states have energy at least b. The Separable Sparse Hamiltonian problem is defined similarly, but the Hamiltonian is not necessarily local, but rather sparse. We show that the Separable Sparse Hamiltonian problem is QMA(2)-Complete, while Separable Local Hamiltonian is in QMA. This should be compared to the Local Hamiltonian problem, and the Sparse Hamiltonian problem which are both QMA-Complete. To the best of our knowledge, Separable Sparse Hamiltonian is the first non-trivial problem shown to be QMA(2)-Complete.
UR - https://www.scopus.com/pages/publications/84866497448
U2 - 10.1109/CCC.2012.42
DO - 10.1109/CCC.2012.42
M3 - Conference contribution
AN - SCOPUS:84866497448
SN - 9780769547084
T3 - Proceedings of the Annual IEEE Conference on Computational Complexity
SP - 32
EP - 41
BT - Proceedings - 2012 IEEE 27th Conference on Computational Complexity, CCC 2012
T2 - IEEE Computer Society Technical Committee on Mathematical Foundations of Computing
Y2 - 26 June 2012 through 29 June 2012
ER -