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arXiv · 1603.01546

Thermal stability of two-dimensional Topological Color Code

Razieh Mohseninia
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Abstract

Thermal stability of the Topological Color Code in presence of a thermal bath is studied. We study the Lindblad evolution of the observables in the weak coupling limit of the Born-Markov approximation. The auto-correlation functions of the observables are used as a figure of merit for the thermal stability. We show that all of the observables auto-correlation functions decay exponentially in time. By finding a lower bound of the decay rate, which is a constant independent of the system size, we show that the Topological Color Code is unstable against thermal fluctuations from the bath at finite temperature, even though it is stable at T=0 against local quantum perturbations.

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Razieh Mohseninia. 2016-03-04. Thermal stability of two-dimensional Topological Color Code. https://doi.org/10.1103/physreva.94.022306

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