Entropic Barriers for Two-Dimensional Quantum Memories

TL;DR

This paper introduces a modified two-dimensional quantum memory model with defect lines, demonstrating entropic effects that suppress errors and enhance stability at low temperatures, despite no-go theorems for stable quantum memories.

Contribution

It proposes a novel defect line grid in Kitaev's model that creates an entropic barrier, improving error suppression in 2D quantum memories.

Findings

Super-exponential inverse temperature scaling observed.

Polynomial system size scaling for small systems at low temperatures.

Entropic effects diminish below a certain low temperature.

Abstract

Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic timescales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev's quantum double model where different anyonic excitations carry different masses. This setting produces a complex energy landscape which entropically suppresses the diffusion of excitations that cause logical errors. We show numerically that entropically suppressed errors give rise to super-exponential inverse temperature scaling and polynomial system size scaling for small system sizes over a low-temperature regime. Curiously, these entropic effects are not present below a certain low temperature. We show that we can vary the system to modify this bound and potentially extend the described effects to zero temperature.