Description

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preliminary]1 An Overview on Quantum Codes1.1 Previous Results1.2 Goals1.3 Some Classes of Quantum Error-Correcting Codes1.4 Quantum Error-Correcting Codes1.4.1 Formalism of Stabilizer Codes1.5 Topological Quantum Codes1.5.1 Topological Stabilizer Codes1.6 CSS Codes1.7 Surface Codes1.8 Toric Quantum Code, g = 11.9 Hyperbolic Surface Codes, g >= 21.10 Color Codes
2 Preliminaries2.1 Upper Half-Plane Model2.2 Unit Open Disc Model2.3 Geometrical Properties in H2 and Delta]2.4 Tessellations in Euclidean and Hyperbolic Planes
3 Surface Codes 293.1 Toric Codes, g = 13.2 Projective Plane Codes, g = 03.3 Homological Quantum Codes, g = 13.4 g-Toric Codes, g >= 2
4 Color Codes4.1 Quantum Color Codes4.2 Hyperbolic Color Codes4.3 Polygonal Color Codes