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arXiv · 1601.01324

Self correction requires Energy Barrier for Abelian quantum doubles

Anna Komar·Olivier Landon-Cardinal·Kristan Temme
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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.

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Anna Komar, Olivier Landon-Cardinal, Kristan Temme. 2016-01-06. Self correction requires Energy Barrier for Abelian quantum doubles. https://doi.org/10.1103/physreva.93.052337

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