Review PaperNo Access

A pedagogical overview on 2D and 3D Toric Codes and the origin of their topological orders

M. F. Araujo de Resende

Instituto de Física, Universidade de São Paulo, 05508-090 São Paulo SP, Brazil

https://doi.org/10.1142/S0129055X20300022Cited by:7 (Source: Crossref)

Abstract

In this work, we will show how the topological order of the Toric Code appears when the lattice on which it is defined discretizes a three-dimensional torus. In order to do this, we will present a pedagogical review of the traditional two-dimensional Toric Code, with an emphasis on how its quasiparticles are conceived and transported. With that, we want to make clear not only how all these same quasiparticle conception and transportation fit into this three-dimensional model, but to make it clear how topology controls the degeneracy of ground state in this new situation.

Keywords:

AMSC: 22E46, 53C35, 57S20

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