Quick Navigation

Topics

Quantum Simulation

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.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2014 reference point for readers tracking recent quantum research.
  • We show that the two-dimensional (2D) local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete.

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

Local Citation Graph (Related-Paper Links)

Current Paper #46293 #69978 Distribution Complexity of Elec... #69974 Hierarchical separation of rela... #69964 Bounded-depth spacetime lattice... #69945 Phase Stable Integrated Delay L...

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0
Likes: 0 Dislikes: 0

Sign in to react to this paper.

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.