Local topological order inhibits thermal stability in 2D

TL;DR

This paper shows that in 2D quantum systems, local topological order prevents the existence of a large energy barrier, thereby limiting the thermal stability of stored quantum information.

Contribution

It establishes a fundamental link between local topological order and the inability to achieve thermal stability in 2D quantum systems.

Findings

Local topological order implies a constant energy barrier.

Constant energy barrier inhibits thermal stability.

Topological order does not guarantee protection against thermal fluctuations.

Abstract

We study the robustness of quantum information stored in the degenerate ground space of a local, frustration-free Hamiltonian with commuting terms on a 2D spin lattice. On one hand, a macroscopic energy barrier separating the distinct ground states under local transformations would protect the information from thermal fluctuations. On the other hand, local topological order would shield the ground space from static perturbations. Here we demonstrate that local topological order implies a constant energy barrier, thus inhibiting thermal stability.