Thermal stability of the two-dimensional topological color code
Razieh Mohseninia · Physical Review A · 2016
Thermal stability of the topological color code in the 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 autocorrelation functions of the observables are used as a figure of merit for the thermal stability. We show that all of the observables autocorrelation 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.