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Two-dimensional local Hamiltonian problem with area laws is QMA-complete
arXiv
Authors: Yichen Huang
Year
2014
Paper ID
46293
Status
Preprint
Abstract Read
~2 min
Abstract Words
93
Citations
N/A
Abstract
We show that the two-dimensional (2D) local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete. We also prove similar results in 2D translation-invariant systems and for the 3D Heisenberg and Hubbard models with local magnetic fields. Consequently, unless MA = QMA, not all ground states of 2D local Hamiltonians with area laws have efficient classical representations that support efficient computation of local expectation values. In the future, even if area laws are proved for ground states of 2D gapped systems, the computational complexity of these systems remains unclear.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We show that the two-dimensional (2D) local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete.
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