Two-dimensional local Hamiltonian problem with area laws is QMA-complete
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.
Keywords
Cite
@article{arxiv.1411.6614,
title = {Two-dimensional local Hamiltonian problem with area laws is QMA-complete},
author = {Yichen Huang},
journal= {arXiv preprint arXiv:1411.6614},
year = {2021}
}
Comments
v2: conference version; v3: journal version with improved presentation (thanks to the reviewers' suggestions). 20-minute video presentation: https://youtu.be/CKwt_pqLOVM