Topological Quantum Memory at Finite Temperature
Alioscia Hamma, Claudio Castelnovo, Claudio Chamon · arXiv (Cornell University) · 2008
We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is possible to store quantum information for macroscopic times without intervention from the external world, that is, without error correction. We study the toric code in 2D with an additional bosonic field that couples to the defects, in presence of a generic environment at finite temperature: the \emph{toric-boson model}. We show that, in the topological phase, there is a critical 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. We argue that the true meaning of quantum topological order at finite temperature is given by the existence of a robust quantum memory.