Toric-boson model: Toward a topological quantum memory at finite temperature

TL;DR

This paper investigates the potential for stable topological quantum memory at finite temperature using a toric-boson model, showing that under certain conditions, memory lifetime can be extended arbitrarily.

Contribution

It introduces a toric-boson model demonstrating finite-temperature stability of topological quantum memory with confined open strings and preserved topological order.

Findings

Open strings are confined below a finite temperature.

Memory lifetime can be made arbitrarily long in system size.

Topological order remains intact despite bosonic interactions.

Abstract

We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the intervention from the external world, that is, without error correction. We study the toric code in two dimensions with an additional bosonic field that couples to the defects, in the presence of a generic environment at finite temperature: the toric-boson model. Although the coupling constants for the bare model are not finite in the thermodynamic limit, the model has a finite spectrum. We show that in the topological phase, there is a finite temperature below which open strings are confined and therefore the lifetime of the memory can be made arbitrarily (polynomially) long in system size. The interaction with the bosonic field yields a long-range attractive force between the end points of open strings but leaves closed strings and topological order intact.