Self-Correcting Quantum Memory in a Thermal Environment

TL;DR

This paper proposes 2D spin models with long-range interactions that enable self-correcting quantum memories at finite temperatures, overcoming previous instability issues due to thermal fluctuations.

Contribution

Introduction of 2D spin models with repulsive long-range interactions that achieve polynomially increasing memory lifetime, demonstrating stable quantum memory at finite temperatures.

Findings

Memory lifetime increases polynomially with system size.

Long-range interactions provide stability against thermal fluctuations.

Numerical simulations support analytical results.

Abstract

The ability to store information is of fundamental importance to any computer, be it classical or quantum. To identify systems for quantum memories which rely, analogously to classical memories, on passive error protection (`self-correction') is of greatest interest in quantum information science. While systems with topological ground states have been considered to be promising candidates, a large class of them was recently proven unstable against thermal fluctuations. Here, we propose two-dimensional (2D) spin models unaffected by this result. Specifically, we introduce repulsive long-range interactions in the toric code and establish a memory lifetime polynomially increasing with the system size. This remarkable stability is shown to originate directly from the repulsive long-range nature of the interactions. We study the time dynamics of the quantum memory in terms of diffusing anyons and support our analytical results with extensive numerical simulations. Our findings demonstrate that self-correcting quantum memories can exist in 2D at finite temperatures.