Değıştirilmiş torik kodunun düşük sıcaklık devinimleri hakkında araştırma

Topological quantum systems were introduced as an attempt to overcome the challenge of decoherence due to the self-correcting properties of their energy eigenstates. One of the simplest and most popular topologically ordered systems is known as ``Kitaev's toric code.'' We study the dynamics of the quasiparticle excitations that live on the two-dimensional surface of the toric code in the zero temperature limit. We also look at a modified version of the toric code in which the continuity of the system is retained in one direction and removed in the other, thus forming a cylindrical surface. We argue that the main process that can result in a logical error in this limit would be a random walker of quasiparticles that can move around the surface in a topologically non-trivial manner. Using a discrete Monte Carlo method, we find the probability of the occurrence of a logical error as a function of the number of steps taken by the walker and the system size. We find that the cylindrical code does indeed show a notable advantage in its passive fault-tolerance when compared to the toric code.