Toric code
Topological quantum error correcting code / From Wikipedia, the free encyclopedia
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The toric code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice.[1] It is the simplest and most well studied of the quantum double models.[2] It is also the simplest example of topological order—Z2 topological order (first studied in the context of Z2 spin liquid in 1991).[3][4] The toric code can also be considered to be a Z2 lattice gauge theory in a particular limit.[5] It was introduced by Alexei Kitaev.
The toric code gets its name from its periodic boundary conditions, giving it the shape of a torus. These conditions give the model translational invariance, which is useful for analytic study. However, some experimental realizations require open boundary conditions, allowing the system to be embedded on a 2D surface. The resulting code is typically known as the planar code. This has identical behaviour to the toric code in most, but not all, cases.