|2D Local Hamiltonian with Area Laws is QMA-Complete
|Yichen Huang, Massachusetts Institute of Technology, United States
|Q.4: Quantum Information Theory
|Quantum Systems, Codes, and Information
|Click here to download the manuscript
|Click here to watch in the Virtual Symposium
|We show that the 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.