Two-dimensional local Hamiltonian problem with area laws is QMA-complete

JOURNAL OF COMPUTATIONAL PHYSICS

卷:443

Article

Huang, Yichen^1,2 

[1] Univ Calif Berkeley, Dept Phys, Berkeley, CA 94720 USA

[2] MIT, Ctr Theoret Phys, Cambridge, MA 02139 USA

关键词: Area law;    Entanglement entropy;    Local Hamiltonian problem;    Quantum many-body physics;    QMA-complete;   

DOI  :  10.1016/j.jcp.2021.110534

来源: Elsevier

【 摘 要 】

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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free