Self correction requires Energy Barrier for Abelian quantum doubles

Abstract

We rigorously establish an Arrhenius law for the mixing time of quantum doubles based on any Abelian group ${\mathbb{Z}}_d$. We have made the concept of the energy barrier therein mathematically well-defined, it is related to the minimum energy cost the environment has to provide to the system in order to produce a generalized Pauli error, maximized for any generalized Pauli errors, not only logical operators. We evaluate this generalized energy barrier in Abelian quantum double models and find it to be a constant independent of system size. Thus, we rule out the possibility of entropic protection for this broad group of models.

18 pages, 6 figures

References in corpus (4)

• Local stabilizer codes in three dimensions without string logical operators
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• 3-d topological quantum memory with a power-law energy barrier
• Can long-range interactions stabilize quantum memory at nonzero temperature?

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