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Topological Quantum Computing
A pedagogical overview on 2D and 3D Toric Codes and the origin of their topological orders
arXiv
Authors: M. F. Araujo de Resende
Year
2017
Paper ID
24753
Status
Preprint
Abstract Read
~2 min
Abstract Words
94
Citations
N/A
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.
Why This Paper Matters
- This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
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- 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.
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